Respuesta :
Assuming the gas in question behaves as an ideal gas, 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, R is the Ideal Gas Constant and T is the absolute temperature.
We have to match the units from R and the other variables.
The pressure is in kPa, so we can look for a R value that is also in kPa.
One such value is:
[tex]R\approx8.31446\frac{L\cdot kPa}{K\cdot mol}[/tex]But the volume unit is in L, so we need to convert the volume we have:
[tex]V=604mL=0.604L[/tex]Now, we have:
[tex]\begin{gathered} P=100.4kPa \\ V=0.604L \\ n=0.0851mol \\ R\approx8.31446\frac{L\cdot kPa}{K\cdot mol} \end{gathered}[/tex]Solving the equation for T and substituting the values, we have:
[tex]\begin{gathered} PV=nRT \\ T=\frac{PV}{nR} \\ T=\frac{100.4\cdot kPa\cdot0.604\cdot L}{8.31446\cdot L\cdot kPa\cdot K^{-1}\cdot mol^{-1}\cdot0.0851mol} \\ T=\frac{100.4\cdot0.604}{8.31446^{}^{}\cdot0.0851}K \\ T=\frac{60.6416}{0.707560\ldots}K \\ T=85.70517\ldots K \\ T\approx85.7K \end{gathered}[/tex]So, the temperature is approximately 85.7 K.
