Question

A pneumatic cylinder contains 75.0 mL of air at atmospheric pressure and a temperature of 35 degrees Celsius. If the pressure is held constant, calculate the volume of the air if it is cooled to a temperature of 10 degrees Celsius.

Answer 1

We will have the following:

First, we are given:

`\begin{gathered} V=75.0mL \\ P=1atm\text{ \lparen constant\rparen} \\ T_i=35C \\ T_f=10C \\ \end{gathered}`

Now, we transform these units to the SI, that is:

`\begin{gathered} V=0.075L \\ P=1atm \\ T_i=308.15K \\ T_f=238.15K \end{gathered}`

Now, using the initial values we determine the quantity of the the gas:

`\begin{gathered} PV=nRT\Rightarrow(1atm)(0.075L)=n(0.082057L\ast atm/K\ast mol)(308.15K) \\ \\ \Rightarrow n=((1atm)(0.075L))/((0.082057L\ast atm/K\ast mol)(308.15K))\Rightarrow n=2.966084068\ast10^(-3)mol \\ \\ \Rightarrow n\approx3.0\ast10^(-3)mol \end{gathered}`

Now that we have the number of moles, then we determine the final volume, that is:

`\begin{gathered} V\approx((3.0\ast10^(-3)mol)(0.082057L\ast atm/K\ast mol)(238.15K))/((1atm))\Rightarrow V\approx0.05862562365L \\ \\ \Rightarrow V\approx0.06L \end{gathered}`

So, the final volume will be approximately 0.06 L.