Question

The volume of an enclosed gas (at a constant pressure) varies directly as the absolute temperature. If the pressure of a 3.46-L sample of neon gas at 302°K is 0.926 atm, what would the volume be at a temperature of 338°K if the pressure does not change?

Answer 1

`3.87L`

Explanation:

Interesting practical (and very common) chemistry problem for an algebraic example! This one is not providing the actual Ideal Gas Law equation, but showing how a part of it (Charles' Law) is derived from the experimental data.

Algebraically, we are told that the rate (slope of the line) is constant with respect to absolute temperature (the independent variable, usually x-axis) and the volume (dependent variable, or y-axis).

The stipulation of a constant pressure is necessary for correctness, as it is involved in the gas equations as well in reality. Also, the actual equation (`PV = nRT`) can interchange any of the factor for either dependent or independent variables. In this case, it means that the "data" of the actual pressure is irrelevant to this problem.

We have two temperatures and an original volume:
`T_1 = 302^oK` ; `V_1 = 3.46L`
`T_2 = 338^oK`

From our relationship description we can construct an equation:
`V_2 = V_1 xx m + b` ; where `m = T_2/T_1` and `b = 0`
`V_2 = V_1 xx T_2/T_1 = 3.46 xx 338/302 = 3.87L`