A 600.0 mL sample of nitrogen is warmed from 77.0 °C to 86.0 °C. Find its new volume (in m3) if the pressure remains constant.

0.000615 m3

Explanation:

Charles's Law

Relationship between the temperature and the volume of a gas when the pressure is constant

In 1787, Jack Charles first studied the relationship between the volume and temperature of a gas sample at constant pressure and observed that when the temperature was increased the volume of the gas also increased and that when the volume cooled, it decreased.

When we increase the temperature of the gas the molecules move faster and take less time to reach the walls of the container. This means that the number of crashes per unit of time will be greater. That is, there will be an increase (for an instant) of the pressure inside the container and the volume will increase (the plunger will move up until the pressure is equalized with the outside).

What Charles discovered is that if the amount of gas and pressure remain constant, the ratio between volume and temperature always has the same value.

Mathematically we can express it like this:

V/T = K

Where:

V: volume

T: temperature

K: constant

Suppose we have a certain volume of V1 gas that is at a temperature T1 at the beginning of the experiment. If we vary the volume of gas to a new V2 value, then the temperature will change to T2, and the following will be true:

V1 / T1 = V2 / T2

Calculation

T1 = 77 °C = 350,15 °K

T2 = 86 °C = 359.15 °K

V1 = 600 mL

V2 = ?

V2 = T2 * (V1 / T1)

V2 = 615 mL = 0.000615 m3