Question

The Celsius temperature of a 4.00-L sample of gas doubles from $\mathbf{20}\mathbf{.}\mathbf{0}\mathbf{°}\mathit{C}$to $\mathbf{40}\mathbf{.}\mathbf{0}\mathbf{°}\mathit{C}$at constant pressure. Determine the volume of the gas after this change.

Short answer

Thus, the final volume of the gas after the change is 4.273 L.

Step-by-step solution

Step-by-step-solutionStep 1: Pressure

The force exerted by a gas on a unit area of the walls of its container is called the pressure of that gas. Pressure is measured with a simple device, called a barometer.

Given Data

The volume of sample of gas is 4 L

Temperature is $20.0°C$to$40.0°C$

Calculation

The final volume of the gas is calculated by using the formula as: $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Here,

*$V_1$is the initial volume of the gas, i.e., 4.00 L.

*$V_2$is the final volume of the gas.

*$T_1$is the initial temperature of the gas, i.e.,.$20.0°C(20.0+273.15)K=293.15K$.

*$T_2$is the final temperature of the gas, i.e., $40.0°C(40.0+273.15)K=313.15K$.

Rearranging and substituting these values, in the given formula we, get

$$\begin{gathered} V_2=\frac{V_1\times T_2}{T_1} \\ =\frac{4.00 L\times 313.15K}{293.15 K} \\ =4.273L \end{gathered}$$

Thus, the final volume of the gas is 4.273 L.