1. 4 g of calcium chloride reacts with excess potassium. Determine the molar enthalpy for the reaction of calcium chloride if in the calorimeter the temperature of the 7. 5 g solution goes from 15 °C to 32 °C. Assume that the solution is mainly water

The atomic weight of the metal is 36 g/mol.

To solve this problem, we need to use the concept of equivalent weight. The equivalent weight of a divalent metal is equal to its atomic weight divided by its valency, which in this case is 2.

First, let's calculate the number of equivalents of H2SO4 present in the solution.

4.9 g of H2SO4 per liter of solution means that there are 4.9/98 = 0.05 moles of H2SO4 per liter.

So in 250 cc (or 0.25 liters) of solution, there are 0.05 x 0.25 = 0.0125 moles of H2SO4.

Since H2SO4 is a diprotic acid, each mole of H2SO4 can donate 2 equivalents of H+. Therefore, the total number of equivalents of H+ present in the solution is 2 x 0.0125 = 0.025.

Now let's calculate the number of equivalents of alkali (which we know is N/10 or 0.1 N) required to neutralize 50 cc of the solution.

20 cc of N/10 alkali is equal to 0.002 equivalents of alkali (since N/10 alkali has a normality of 0.1, which means it can donate 0.1 equivalents of OH- per liter of solution).

Since the acid and alkali react in a 1:1 ratio, this means that there are also 0.002 equivalents of H+ in 50 cc of the solution.

Therefore, the initial number of equivalents of H+ in the solution must have been 0.025 + 0.002 = 0.027.

Now we can use this information to calculate the number of equivalents of metal present in the solution.

Since the metal is divalent, it will donate 2 equivalents of metal ions for every 1 equivalent of H+ that it reacts with.

Therefore, the number of equivalents of metal present in the solution is 0.027/2 = 0.0135.

Finally, we can calculate the atomic weight of the metal using the formula:

Atomic weight = Equivalent weight x Valency

In this case, the equivalent weight is equal to the atomic weight divided by 2 (since the metal is divalent).

So:

Atomic weight = Equivalent weight x 2

Atomic weight = (0.018 g / 0.0135 equivalents) x 2

Atomic weight = 36 g/mol

Therefore, the atomic weight of the metal is 36 g/mol.

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Answer:

Rameshwaram Gandhamadan mountain

The total energy needed to convert the 475.0 grams of water at 40.0°C to steam at 100.0°C is 1,068,637.5 Joules.

The energy needed to change 475.0 grams of liquid water at 40.0°C to steam at 100.0°C is known as the latent heat of vaporization.

This amount of energy is required to overcome the forces that keep the molecules of water in a liquid state. In other words, it is the energy needed to break the bonds that keep the molecules of water in a liquid state.

To calculate the total energy needed, the latent heat of vaporization is multiplied by the mass of water. Therefore, the total energy needed to convert the 475.0 grams of water at 40.0°C to steam at 100.0°C is 1,068,637.5 Joules.

This energy needs to be supplied in the form of heat for the water to change from liquid to steam.

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Because the fourth electron of each carbon atom is unbound, graphite conducts electricity. As a result of the existence of free electrons in the structure, we may deduce that graphite is an excellent conductor of electricity.

The pressure of a gas is 1.2 atm at 300k.  the pressure  at 250k if the gas is in a rigid container is 1.0 atm.

To solve this problem, we can use the combined gas law, which states that:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

where P1 is the initial pressure, V1 is the initial volume (which is constant since the gas is in a rigid container), T1 is the initial temperature, P2 is the final pressure (what we're trying to find), V2 is the final volume (also constant), and T2 is the final temperature.

We can rearrange the equation to solve for P2:

P2 = (P1 * V1 * T2) / (V2 * T1)

Plugging in the given values, we get:

P2 = (1.2 atm * V1 * 250K) / (V2 * 300K)

Since the container is rigid, V1 = V2, so we can cancel those terms:

P2 = (1.2 atm * 250K) / 300K

Simplifying:

P2 = 1.0 atm

Therefore, the pressure of the gas at 250K in a rigid container is 1.0 atm.

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To solve this problem, we need to use the pH formula:

pH = -log[H+]

where [H+] represents the concentration of hydrogen ions in moles per liter (M).

To find [H+], we can rearrange the formula:

[H+] = 10^(-pH)

Substituting pH = 3.69, we get:

[H+] = 10^(-3.69) = 2.21 × 10^(-4) M

Since hydrochloric acid is a strong acid, it completely dissociates in water to give hydrogen ions and chloride ions:

HCl(aq) → H+(aq) + Cl-(aq)

Therefore, the concentration of hydrochloric acid required to give a solution with a pH of 3.69 is also 2.21 × 10^(-4) M.

The temperature of the helium sample changed by approximately 0.0314 degrees Celsius.

To calculate the temperature change of the helium sample, we can use the formula:

q = mcΔT

where q is the heat absorbed (125.7 calories), m is the mass of the sample (634.5 g), c is the specific heat capacity of helium (1.241 cal/(g·°C)), and ΔT is the temperature change in degrees Celsius. We need to find ΔT.

Rearranging the formula to solve for ΔT, we get:

ΔT = q / (mc)

Now, plug in the given values:

ΔT = 125.7 cal / (634.5 g × 1.241 cal/(g·°C))

ΔT ≈ 0.0314 °C

Therefore, the temperature of the helium sample changed by approximately 0.0314 degrees Celsius.

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The correct answer is e. The concentrations of H2 and HI will decrease as the system is approaching equilibrium.

the equilibrium concentration of HI is 1.18 x 10^-4 M.

The correct answer is e. The concentrations of H2 and HI will decrease as the system is approaching equilibrium.

This is because the equilibrium constant, Kc, for the reaction is 64, which is a relatively large value. This suggests that the forward reaction (2HI → H2 + I2) is favored at equilibrium, meaning that the concentration of HI will decrease as the system approaches equilibrium.

To calculate the equilibrium concentration of HI, we can use the equilibrium constant expression:

Kc = [H2][I2]/[HI]^2

Substituting the given values, we get:

64 = (4.2 x 10^-4)(1.9 x 10^-3)/[HI]^2

Solving for [HI], we get:

[HI] = sqrt((4.2 x 10^-4)(1.9 x 10^-3)/64) = 1.18 x 10^-4 M

Therefore, the equilibrium concentration of HI is 1.18 x 10^-4 M.
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The calculation of the mass of SnF₂ present in the toothpaste sample determined it to be 0.105 g. The mass percentage of stannous fluoride in the toothpaste sample was found to be 1.05%. The percent yield of the extraction/recovery process, comparing the recovered mass of SnF₂ to the expected mass based on the percentage listed on the box, was calculated to be 70.0%. This indicates a moderate level of efficiency in the extraction/recovery process.

To solve this problem, we need to use stoichiometry and the concept of percent yield.

1. Calculation of the mass of SnF₂ present in the toothpaste sample:

Let's assume that all the SnF₂ in the toothpaste sample was extracted and precipitated.

The balanced chemical equation for the reaction between stannous fluoride and lanthanum nitrate is:

SnF₂ + 2La(NO₃)3 → La₂(SnF₆) + 6NO₃

According to the equation, 1 mole of SnF₂ reacts with 2 moles of La(NO₃)₃ to form 1 mole of La2(SnF6).

The molar mass of SnF2 is 156.69 g/mol.

Therefore, the number of moles of SnF₂ in the toothpaste sample is:

n(SnF₂) = (0.105 g)/(156.69 g/mol) = 0.0006701 mol

Since the stoichiometric ratio of SnF₂ to La₂(SnF₆) is 1:1, the number of moles of La₂(SnF₆) formed is also 0.0006701 mol.

The mass of SnF2 present in the toothpaste sample is:

m(SnF₂) = n(SnF₂) × M(SnF₂) = 0.0006701 mol × 156.69 g/mol = 0.105 g

Therefore, the mass of SnF₂ present in the toothpaste sample is 0.105 g.

2. Calculation of the mass percentage of stannous fluoride in the toothpaste sample:

The mass percentage of SnF₂ in the toothpaste sample is:

% mass = (mass of SnF₂ / mass of toothpaste sample) × 100%

The mass of the toothpaste sample is given as 10.00 g.

Therefore, the mass percentage of SnF₂ in the toothpaste sample is:

% mass = (0.105 g / 10.00 g) × 100% = 1.05%

Therefore, the mass percentage of stannous fluoride in the toothpaste sample is 1.05%.

3. Analysis of the percent yield of the extraction/recovery process:

The percentage of SnF₂ listed on the box was 1.50%.

The percent yield of the extraction/recovery process is calculated as:

% yield = (mass of SnF₂ recovered / expected mass of SnF₂) × 100%

The expected mass of SnF₂ in the toothpaste sample, based on the percentage listed on the box, is:

mass of SnF₂ expected = (1.50% / 100%) × 10.00 g = 0.150 g

Therefore, the percent yield of the extraction/recovery process is:

% yield = (0.105 g / 0.150 g) × 100% = 70.0%

This means that the efficiency of the extraction/recovery process was 70.0%, which is not very high. It could be due to various factors such as incomplete extraction or loss of SnF₂ during the precipitation process.

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The volume of gas at 140.0 °C is calculated as 1033 ml.

Space occupied by gaseous particles at the standard temperature and pressure conditions is called the volume of gas

T1 = 32.0 °C + 273.15 = 305.15 K

T2 = 140.0 °C + 273.15 = 413.15 K

Next, we can set up the proportion: V1/T1 = V2/T2

V1 is initial volume, V2 is final volume, T1 is initial temperature, and T2 is final temperature.

762.0 mL/305.15 K = V2/413.15 K

V2 = 762.0 mL × (413.15 K/305.15 K) = 1033 mL

Therefore, the volume of the gas at 140.0 °C is 1033 ml.

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NAD+ is the most common electron carrier needed for both glycolysis and the citric acid cycle. It is a coenzyme and is involved in redox reactions.

It is an oxidized form of NADH, which is the reduced form. During the oxidation of organic molecules, NAD+ will accept electrons and become NADH. During the reduction of organic molecules, NADH will give electrons and become NAD+.

During glycolysis, NAD+ is used to accept electrons from the oxidation of glucose, creating NADH and releasing energy for the ATP production. During the citric acid cycle, NAD+ accepts electrons from the oxidation of acetyl CoA, creating NADH and releasing energy for the ATP production. The NADH produced in both glycolysis and the citric acid cycle can be used in the electron transport chain to produce ATP.

In summary, NAD+ is an oxidized form of NADH and it is essential in both glycolysis and the citric acid cycle to produce energy in the form of ATP.

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Enter your numerical answer with the correct number of significant figures: 5.24 moles.

Moles are small mammals that are known for their distinctive black or brown fur and their burrowing habits. They belong to the family Talpidae and are found in many parts of the world including North America, Europe, and some parts of Asia. Moles have small eyes and ears, short legs, and a long, cylindrical body. They typically measure around 3 to 5 inches in length and weigh around 1 to 4 ounces. They feed mostly on earthworms and other small invertebrates, and their diet is supplemented by insects, eggs, and other small animals. Moles have specialized claws and feet which allow them to dig quickly and efficiently.

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Answer:

They forge heavy elements in their cores, explode as supernovas, and expel these elements into space.

Explanation:

When a 27. 7 g sample of ethylene glycol (C = 2. 42 J/gºC) at 42. 76°C is cooled to 32. 5°C the amount of heat released is  685.87 joule.

To calculate the heat released when a 27.7 g sample of ethylene glycol is cooled from 42.76°C to 32.5°C, you can use the formula:

q = mcΔT

where q represents the heat released, m is the mass (27.7 g), c is the specific heat capacity (2.42 J/gºC), and ΔT is the change in temperature (42.76°C - 32.5°C).

ΔT = 42.76°C - 32.5°C = 10.26°C

Now plug in the values into the formula:

q = (27.7 g) × (2.42 J/gºC) × (10.26°C) = 685.87 J

So, 685.87 Joules of heat are released when the 27.7 g sample of ethylene glycol is cooled from 42.76°C to 32.5°C.

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In the electrowinning process, the energy applied using 5 mol of IR photons with a wavelength of 32 nm is 1.863 MJ.

1. Convert wavelength to energy using the equation: E = (hc)/λ, where h is Planck's constant (6.626×10⁻³⁴ Js), c is the speed of light (3×10⁸ m/s), and λ is the wavelength (32 nm = 32×10⁻⁹ m).

2. Calculate the energy of one IR photon: E = (6.626×10⁻³⁴ Js × 3×10⁸ m/s) / (32×10⁻⁹ m) = 6.184×10⁻¹⁹ J.

3. Determine the energy for 5 moles of IR photons: Total energy = 6.184×10⁻¹⁹ J × 5 × 6.022×10²³ photons/mol = 1.863×10⁶ J.

4. Convert energy to megajoules: 1.863×10⁶ J = 1.863 MJ.

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Answer: H2O2

Explanation: The formula that represents hydrogen peroxide is H2O2

The solubility product constant (Ksp) for Ag2CrO4 is given by the following equation:

Ag2CrO4(s) ⇌ 2Ag+(aq) + CrO4^(2-)(aq)

The expression for Ksp is:

Ksp = [Ag+]^2[CrO4^(2-)]

where [Ag+] and [CrO4^(2-)] are the concentrations of the silver ion and chromate ion in the equilibrium mixture, respectively.

To determine the value of Q, the reaction quotient, we need to determine the concentrations of Ag+ and CrO4^(2-) in the mixture of 5.00 mL of 0.0040 M AgNO3 and 4.00 mL of 0.0024 M K2CrO4. To do this, we need to make some assumptions:

1. The volumes of the two solutions are additive, so the total volume is 9.00 mL.

2. The AgNO3 and K2CrO4 solutions react completely to form Ag2CrO4.

First, we need to determine the moles of Ag+ and CrO4^(2-) in each solution:

For the AgNO3 solution:

moles of Ag+ = (0.0040 M) x (0.00500 L) = 2.0 x 10^-5 mol

For the K2CrO4 solution:

moles of CrO4^(2-) = (0.0024 M) x (0.00400 L) = 9.6 x 10^-6 mol

Since the AgNO3 and K2CrO4 react in a 1:1 ratio to form Ag2CrO4, the limiting reactant is K2CrO4. Therefore, all of the CrO4^(2-) is used up in the reaction, and the concentration of CrO4^(2-) in the equilibrium mixture is zero.

The concentration of Ag+ in the equilibrium mixture is:

[Ag+] = moles of Ag+ / total volume of mixture

[Ag+] = (2.0 x 10^-5 mol) / (9.00 x 10^-6 L)

[Ag+] = 2.22 M

Now, we can calculate the value of Q:

Q = [Ag+]^2[CrO4^(2-)] = (2.22 M)^2(0 M) = 0

Since Q is equal to zero and Ksp is greater than zero (1.8 x 10^-10), the reaction is not at equilibrium and Ag2CrO4 will precipitate from the solution.

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Answer:

when u stop at great speed in a vechial your body is in still in motion

Explanation:

Answer:

320.3 grams of SO2 can be produced

Explanation:

In order to calculate the amount of SO2 produced, we first need to write a balanced chemical equation for the reaction between O2 and sulfur:

2 SO2 + O2 -> 2 SO3

From the equation, we can see that 1 molecule of O2 reacts with 2 molecules of SO2 to produce 2 molecules of SO3.

Therefore, we need to convert the number of O2 molecules to the number of SO2 molecules in order to calculate the amount of SO2 produced.

1 molecule of O2 reacts with 2 molecules of SO2, so:

2.5 molecules of O2 * (2 molecules of SO2 / 1 molecule of O2) = 5 molecules of SO2

Now that we have the number of SO2 molecules produced, we can calculate the mass of SO2 using its molar mass. The molar mass of SO2 is approximately 64.06 g/mol.

5 molecules of SO2 * (64.06 g/mol) = 320.3 grams of SO2

Therefore, if 2.5 molecules of O2 react with sulfur to form SO2, then 320.3 grams of SO2 can be produced.

The weight of NaCl in a 0.500 L bottle of 2.00 M NaCl solution is 58.44 grams.

To calculate the weight of NaCl in a 0.500 L bottle of 2.00 M NaCl solution, we need to use the formula:

Mass = Moles x Molar mass

First, let's calculate the number of moles of NaCl in the solution:

Moles = Molarity x Volume

Moles = 2.00 mol/L x 0.500 L

Moles = 1.00 mol

The molar mass of NaCl is 58.44 g/mol, so we can now calculate the mass of NaCl in the solution:

Mass = moles x molar mass

Mass = 1.00 mol x 58.44 g/mol

Mass = 58.44 g

Therefore, the weight of NaCl in a 0.500 L bottle of 2.00 M NaCl solution is 58.44 grams.

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The concentration of the NaOH solution is approximately 0.00624 M.

To find the concentration of the NaOH solution, you can use the titration formula:

M1V1 = M2V2

where M1 is the concentration of HCl (0.010 M), V1 is the volume of HCl (15.6 mL), M2 is the concentration of NaOH (unknown), and V2 is the volume of NaOH (25.0 mL).

0.010 M * 15.6 mL = M2 * 25.0 mL

Now, solve for M2:

M2 = (0.010 M * 15.6 mL) / 25.0 mL
M2 ≈ 0.00624 M

So, the concentration of the NaOH solution is approximately 0.00624 M.

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In the field of chemistry, the term "conjugate" is used to describe pairs of molecules or ions that are connected through the transfer of a proton, which is represented as H⁺. Conjugate acids and bases, specifically, are pairs of molecules or ions that vary by the presence or absence of one proton.

These equilibrium equations represent the transfer of a proton between a weak acid or base and water, resulting in the formation of its conjugate acid or base.

Answer of the given questions are as follows :

1. The formula of the conjugate acid: HCO₂H

2. The formula of the conjugate base: C₆HNH₃⁺

3. The formula of the conjugate acid of the brønsted-lowry base: H₂CO₃

4. The formula of the conjugate acid of the brønsted-lowry base:

C₆H₅NH₃⁺

5. The acidic equilibrium equation for HC₂H₃O₂: HC₂H₃O₂ + H₂O ⇌ H₃O⁺ + C₂H₃O²⁻

6. The basic equilibrium equation for C₆H₅NH₂

C₆H₅NH₂ + H₂O ⇌ C₆H₅NH₃⁺ + OH⁻

7. The basic equilibrium equation for NH₃

NH₃ + H₂O ⇌ NH₄⁺ + OH⁻

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The type of reaction for the given equation is a double displacement reaction, where the sodium bicarbonate and citric acid react to form sodium citrate and carbonic acid. The carbonic acid then undergoes a decomposition reaction to produce water and carbon dioxide. This type of reaction is called a decomposition reaction.

The symbols inside the parentheses after the formula of the compounds represent the chemical structure of the molecule. In the case of citric acid, the parentheses indicate the presence of three carboxylic acid functional groups, which are responsible for its acidity.

The presence of these groups also allows for the reaction with sodium bicarbonate to occur, forming sodium citrate and carbonic acid. Overall, this reaction demonstrates the principles of acid-base chemistry and the importance of understanding chemical structures in predicting reactions.

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The volume of the balloon after the dry ice sublimes will be 3.40 L at STP.

The balanced chemical equation for the sublimation of solid CO₂ is:

CO₂(s) → CO₂(g)

At STP (standard temperature and pressure), which is 0°C (273.15 K) and 1 atm (101.325 kPa), one mole of any ideal gas occupies 22.4 L of volume. We can use this information to calculate the volume of CO₂ gas produced by the sublimation of 7.00 g of dry ice.

First, we need to convert the mass of dry ice to moles of CO₂ using the molar mass of CO₂, which is 44.01 g/mol:

7.00 g CO₂ × (1 mol CO₂/44.01 g CO₂) = 0.159 moles CO₂

Next, we can use the ideal gas law to calculate the volume of CO₂ gas produced:

PV = nRT

where P is the pressure (1 atm), V is the volume we want to find, n is the number of moles of CO₂ (0.159 moles), R is the gas constant (0.08206 L·atm/mol·K), and T is the temperature (273.15 K):

V = nRT/P = (0.159 mol)(0.08206 L·atm/mol·K)(273.15 K)/(1 atm) = 3.40 L

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The percent yield for the reaction of 1.23 g of aluminum with excess sulfuric acid to produce 3.00 g of aluminum sulfate is 38.46%.

To find the percent yield for the reaction of aluminum with sulfuric acid to produce aluminum sulfate, you need to follow these steps:

1. Write the balanced chemical equation for the reaction:
2 Al + 3 H₂SO₄ → Al₂(SO₄)₃ + 3 H₂

2. Calculate the molar mass of aluminum (Al) and aluminum sulfate (Al₂(SO₄)₃):
Al: 26.98 g/mol
Al₂(SO₄)₃: (2 × 26.98) + (3 × [4 × 16.00 + 32.07]) = 53.96 + 342.15 = 342.15 g/mol

3. Determine the moles of aluminum used in the reaction:
moles of Al = mass of Al / molar mass of Al = 1.23 g / 26.98 g/mol = 0.0456 mol

4. Calculate the theoretical yield of aluminum sulfate based on the moles of aluminum:
moles of Al₂(SO₄)₃ = 0.0456 mol Al × (1 mol Al₂(SO₄)₃ / 2 mol Al) = 0.0228 mol Al₂(SO₄)₃
mass of Al₂(SO₄)₃ = moles of Al₂(SO₄)₃ × molar mass of Al₂(SO₄)₃ = 0.0228 mol × 342.15 g/mol = 7.80 g (theoretical yield)

5. Calculate the percent yield:
percent yield = (actual yield / theoretical yield) × 100% = (3.00 g / 7.80 g) × 100% = 38.46%

So, the percent yield for the reaction of 1.23 g of aluminum with excess sulfuric acid to produce 3.00 g of aluminum sulfate is 38.46%.

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The concentration of Cu(OH) is 0.185 M.

To find the concentration of Cu(OH), we need to use the balanced chemical equation for the neutralization reaction:
Cu(OH)₂ + 2 H₂(C₂₀₄)  → Cu(C₂₀₄) )₂ + 4H2O

From the equation, we can see that 2 moles of  H₂(C₂₀₄)  react with 1 mole of Cu(OH)₂.

Therefore, we can use the following equation to calculate the moles of Cu(OH)₂:
moles of Cu(OH)₂ = moles of  H₂(C₂₀₄) / 2

To find the moles of  H₂(C₂₀₄) , we can use the concentration and volume of the H₂(C₂₀₄)  solution:
moles of  H₂(C₂₀₄)  = concentration of  H₂(C₂₀₄)  x volume of  H₂(C₂₀₄)  (in liters)

We need to convert the volume of the  H₂(C₂₀₄)  solution from milliliters to liters:
volume of  H₂(C₂₀₄)  = 47.8 mL = 0.0478 L

Substituting the given values, we get:
moles of H₂(C₂₀₄) = 0.56 M x 0.0478 L = 0.026768 moles

Now we can calculate the moles of Cu(OH)₂:
moles of Cu(OH)₂ = 0.026768 moles / 2 = 0.013384 moles

To find the concentration of Cu(OH), we need to divide the moles of Cu(OH)₂ by the volume of the Cu(OH) solution in liters:
concentration of Cu(OH) = moles of Cu(OH)₂ / volume of Cu(OH) (in liters)

We need to convert the volume of the Cu(OH) solution from milliliters to liters:
volume of Cu(OH) = 72.4 mL = 0.0724 L

Substituting the calculated values, we get:
concentration of Cu(OH) = 0.013384 moles / 0.0724 L = 0.185 M
Therefore, the concentration of Cu(OH) is 0.185 M.

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The commonly used rules of thumb used by chemists to make buffers are:

Buffers are solutions that resist changes in pH when small amounts of acid or base are added to them. They are commonly used in many chemical and biological applications. The rules of thumb mentioned above provide guidelines for making effective buffers. Rule a) ensures that there is an adequate amount of buffering capacity in the solution. Rule b) is based on the fact that weak acids have a pH-dependent dissociation constant, and therefore, the pH of a buffer made from a weak acid will be close to the pKa of the weak acid.

Similarly, the pH of a buffer made from a weak base will be close to the pKa of the conjugate acid. Rule c) ensures that the buffering capacity of the solution is optimized by selecting the appropriate pKa value. Overall, these rules of thumb help chemists to design effective buffers that can maintain a stable pH over a range of conditions.

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One simple experiment that can be conducted to demonstrate that living materials contain water is heating of simple matter.

The following experimental procedure deminstrates the presence of water on living matter.

If the sample contains water, the final weight will be less than the initial weight, indicating that some of the water has been lost due to the heating process.

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186.48 g of [tex]Na_2CS_3[/tex] were generated throughout the reaction.

The balanced chemical equation is:

[tex]3CS_2[/tex] + 6NaOH → [tex]2Na_2CS_3[/tex] + NaOH + [tex]3H_2O[/tex]

The molar mass of [tex]CS_2[/tex] is 76.14 g/mol, and the molar mass of [tex]2Na_2CS_3[/tex] is 192.23 g/mol.

To find the limiting reactant, we need to calculate the number of moles of each reactant. Using the given mass of [tex]CS_2[/tex]:

110.88 g [tex]CS_2[/tex] / 76.14 g/mol = 1.456 mol [tex]CS_2[/tex]

Using the given number of moles of [tex]NaOH[/tex]:

3.12 mol [tex]NaOH[/tex]

We can see that [tex]CS_2[/tex] is the limiting reactant, since it has fewer moles than [tex]NaOH[/tex]. Therefore, we will use the amount of [tex]CS_2[/tex] to calculate the amount of [tex]Na_2CS_3[/tex] produced.

From the balanced equation, we can see that 3 mol of [tex]CS_2[/tex] produces 2 mol of [tex]Na_2CS_3[/tex]. So, 1.456 mol of [tex]CS_2[/tex] will produce:

(2 mol [tex]Na_2CS_3[/tex] / 3 mol [tex]CS_2[/tex]) * 1.456 mol [tex]CS_2[/tex] = 0.971 mol [tex]Na_2CS_3[/tex]

Now, we can use the molar mass of [tex]Na_2CS_3[/tex] to calculate the mass produced:

0.971 mol [tex]Na_2CS_3[/tex] * 192.23 g/mol = 186.48 g [tex]Na_2CS_3[/tex]

Therefore, the mass of [tex]Na_2CS_3[/tex] produced in the reaction is 186.48 g.

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After four half-lives, 12.5 grams of the parent isotope will be left in a sample that originally contained 140 grams of an unstable isotope.

The amount of the parent isotope remaining after a certain number of half-lives can be calculated using the formula:

Remaining amount = Initial amount x (1/2)^(number of half-lives)

For this problem, the initial amount of the unstable isotope is 140 g, and it goes through 4 half-lives.

One half-life is the time it takes for half of the original sample to decay, and the number of half-lives is equal to the total time elapsed divided by the length of one half-life.

If we know the half-life of the isotope, we can find the total time elapsed. Let's assume the half-life of the isotope is 10 days.

After 10 days, half of the initial sample will remain:

Remaining amount = 140 g x (1/2)¹ = 70 g

After another 10 days (20 days total), half of the remaining sample will decay:

Remaining amount = 70 g x (1/2)¹ = 35 g

After another 10 days (30 days total), half of the remaining sample will decay again:

Remaining amount = 35 g x (1/2)¹ = 17.5 g

After another 10 days (40 days total), half of the remaining sample will decay once more:

Remaining amount = 17.5 g x (1/2)¹ = 8.75 g

Therefore, after 4 half-lives (40 days), there will be approximately 8.75 g of the parent isotope remaining.

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