Question

A cylinder fitted with a movable piston and filled with a gas has a volume of 16.44 liters at 22.4°C when the applied pressure is 772.2 torr.
The temperature of the oil bath surrounding the piston was increased to 184.4°C, and the pressure on the piston was changed. Careful measurement now gave a value of 39.03 liters for the new volume.

What is the final pressure in the cylinder, expressed in torr?

a) 494.0 torr

b) 503.6 torr

c) 1184 torr

d) 1207 torr

e) 6295 torr

with explanation please.

Answer 1

Answer:

b) 503.6 torr

Explanation:

Given data

• Initial volume (V₁): 16.44 L

• Initial temperature (T₁): 22.4°C + 273.15 = 295.6 K

• Initial pressure (P₁): 772.2 torr

• Final volume (V₂): 39.03 L

• Final temperature (T₂): 184.4°C + 273.15 = 457.6 K

• Final pressure (P₂): ?

We can find the final pressure applying the combined gas law.

$\frac{P_{1}V_{1}}{T_{1}} =\frac{P_{2}V_{2}}{T_{2}}\\\frac{772.2torr\times 16.44L }{295.6K}=\frac{P_{2}\times 39.03 L }{457.6K}  \\P_{2}=503.6 torr$