A gas cylinder filled with argon is kept at a pressure of 177 atm and 25 degrees C. What is the gas pressure when the temperature of the cylinder and its contents are heated to 195 degrees C by exposure to fire?

Answers

Answer 1

Answer:

278 atm

Explanation:

We're gonna use this formula: [tex]\frac{P_1}{T_1} =\frac{P_2}{T_2}[/tex]

P₁ = 177 atm

T₁ = 298 (Convert Celsius to kelvins by adding 273)

P₂ = ?

T₂ = 468 (195 + 273)

We got

[tex]\frac{177}{298} =\frac{P_2}{468}[/tex]

We can cross-multiply or multiply both sides by 468

I'm gonna go with the latter

[tex](468)\frac{177}{298} =\frac{P_2}{468}(468)[/tex]

[tex]P_2 = \frac{(468)(177)}{298}[/tex]

[tex]P_2 = 277.973[/tex]

Answer 2

Answer:

[tex]\boxed {\boxed {\sf 278 \ atm}}[/tex]

Explanation:

We are asked to find the gas pressure when the temperature of a gas is changed. We will use Gay-Lussac's Law, which states the pressure of a gas is proportional to the temperature of the gas. The formula for this law is:

[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]

Initially, the pressure is 177 atmospheres and the temperature is 25 degrees Celsius or 298 Kelvin.

[tex]\frac {177 \ atm}{298 \ K}=\frac{P_2}{T_2}[/tex]

Then, the gas cylinder is exposed to fire and the temperature is raised to 195 degrees Celsius or 468 Kelvin, but the pressure is unknown.

[tex]\frac {177 \ atm}{298 \ K }=\frac{P_2}{468 \ K}[/tex]

We are solving for the new pressure, so we must isolate the variable P₂. It is being divided by 468 Kelvin. The inverse operation of division is multiplication, so we multiply both sides of the equation by 468 Kelvin.

[tex]468 \ K *\frac {177 \ atm}{298 \ K}=\frac{P_2}{468 \ K}*468 \ K[/tex]

[tex]468 \ K *\frac {177 \ atm}{298 \ K}=P_2[/tex]

The units of Kelvin cancel.

[tex]468 \ K *\frac {177 \ atm}{298 \ K }=P_2[/tex]

[tex]468 * 0.593959731544 \ atm = P_2[/tex]

[tex]277.973154362 \ atm = P_2[/tex]

The pressure in the cylinder after exposure to fire is approximately 278 atmospheres.


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In brackets, are the reagents

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Answers

Answer:

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[tex].[/tex]

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