Question

A cylinder with a moveable piston

contains 1.20 L of a gas at 45.0
atm and 314 K. The pressure and
temperature increase to 96.0 atm
and 420 K. What is the new
volume of the cylinder?

Answer 1

0.752 L (3 s.f.)

Step-by-step explanation:

A cylinder with a moveable piston contains 1.20 L of a gas at 45.0 atm and 314 K. The pressure and temperature increase to 96.0 atm and 420 K.

To find the new volume of the cylinder, we can use the combined gas law.

Combined Gas Law

`\boxed{\sf (P_1V_1)/(T_1)=(P_2V_2)/(T_2)}`

where:

• P₁ is the initial pressure.
• V₁ is the initial volume.
• T₁ is the initial temperature (in kelvin).
• P₂ is the final pressure.
• V₂ is the final volume.
• T₂ is the final temperature (in kelvin).

The values to substitute into the formula are:

• P₁ = 45.0 atm
• V₁ = 1.20 L
• T₁ = 314 K
• P₂ = 96.0 atm
• T₂ = 420 K

Rearrange the formula to isolate V₂:

`\sf V_2=(P_1V_1T_2)/(T_1P_2)`

Substitute the values into the formula and solve for V₂:

`\sf V_2=(45.0 \; atm \cdot 1.20\;L\cdot 420\;K)/(314\;K\cdot 96.0\;atm)`

`\sf V_2=(22680\;L)/(30144)`

`\sf V_2=0.752388535...\;L`

`\sf V_2=0.752\;L\;(3\;s.f.)`

Therefore, the new volume of the cylinder is 0.752 L (3 s.f.).