To calculate this, we will need to assume the gas behaves as an ideal gas.
So, we can use the Ideal Gas Law:
[tex]PV=nRT[/tex]Where P is the pressure, V is the volume, n is the number of moles, is the absolut temperature and R is the gas law constant.
Since we have carbon dioxide, CO₂, we need to calculate its molar mass to convert the mass to number of moles:
[tex]\begin{gathered} M_{CO_2}=(1\cdot M_C+2\cdot M_O) \\ M_{CO_2}=(1\cdot12.0107+2\cdot15.9994)g\/mol \\ M_{CO_2}=44.0095g\/mol \end{gathered}[/tex]So, the number of moles is:
[tex]\begin{gathered} M_{CO_2}=\frac{m}{n} \\ n=\frac{m}{M_{CO_{2}}}=\frac{5.4g}{44.0095g\/mol}=0.1227\ldots mol\approx0.12mol \end{gathered}[/tex]Also, we need to convert the temperature to absolute temperature, so we can convert it to K by adding 273.15 to the degree celcius temperature:
[tex]T=32.5\degree C=(32.5+273.15)K=305.65K[/tex]Now, we need to use the constant R that has the unit we want. We have K for temperature, mol for number of moles and L for volume. Is we want the pressure in kPa, we need to use the R constant with units L*kPa/(K*mol), which have the value:
[tex]R\approx8.31446\frac{L\cdot kPa}{K\cdot mol}[/tex]So, solving the equation for P and substituting the values, we have:
[tex]\begin{gathered} PV=nRT \\ P=\frac{nRT}{V} \\ P=\frac{0.12mol\cdot8.31446L\cdot kPa\cdot K^{-1}mol^{-1}\cdot305.65K}{20.0L} \\ P=\frac{0.12\cdot8.31446\cdot305.65}{20.0}kPa \\ P=15.247\ldots kPa\approx15kPa \end{gathered}[/tex]So, the pressure is approximately 15 kPa.
