PROBLEM 41P

A 48.3-mL sample of gas in a cylinder equipped with a piston is warmed from 22 °C to 87 °C. What is its volume at the final temperature?

Solution 41P

Given :

Initial Volume of gas (Vi) = 48.3 mL

Initial temperature (Ti) = 22 °C = 22 + 273 = 295 K

Final Temperature (Tf) = 87 °C = 87 + 273 = 360 K

Final volume(Vf) = ?

Charles’s law states that ‘At a fixed pressure, the volume of a gas is directly proportional to the kelvin temperature of the gas.’

Mathematically it can be represented as :

V T Or = k

where:

V = volume of the gas,

T = temperature of the gas (measured in kelvins),

k = constant.

With pressure , it can be represented as :

=

First, Let’s convert volume in mL to L :

1 L = 1000 mL

Hence, 48.3 mL in L is :

= 48.3 mL

= 0.0483 L.

Here, the pressure are assumed to be constant .

Vf =

=

= 0.058 L

Hence final volume is 58 mL or 0.058L