Question

A sample of gas has a density of 0.53 g/L at 225 K and under a pressure of 108.8 kPa. Find the density of the gas at 345 K under a pressure of 68.3 kPa. Assuming the mass is equal to 1 gram.

Answer 1

`\rho _2=0.22g/L`

Step-by-step explanation:

Hello!

In this case, since we are considering an gas, which can be considered as idea, we can write the ideal gas equation in order to write it in terms of density rather than moles and volume:

`PV=nRT\\\\PV=(m)/(MM) RT\\\\P*MM=(m)/(V) RT\\\\P*MM=\rho RT`

Whereas MM is the molar mass of the gas. Now, since we can identify the initial and final states, we can cancel out R and MM since they remain the same:

`(P_1*MM)/(P_2*MM) =(\rho _1RT_1)/(\rho _2RT_2) \\\\(P_1)/(P_2) =(\rho _1T_1)/(\rho _2T_2)`

It means we can compute the final density as shown below:

`\rho _2=(\rho _1T_1P_2)/(P_1T_2)`

Now, we plug in to obtain:

`\rho _2=(0.53g/L*225K*68.3kPa)/(345K*108.8kPa)\\\\\rho _2=0.22g/L`

Regards!