Question

How do you determine the volume if 1.5 atm of gas at \[{{20}^{o}}C\] in a 3.0L vessel are heated to \[{{30}^{o}}C\] at a pressure of a 2.5 atm?

Answer 1

Hint: The combined gas law is derived from the ideal gas law. the combined gas law was formed by the Charles law, Boyles law and Gay Lussac law. whereas the ideal gas law has been derived from the charles law, boyle's law and Avogadro law. The ideal gas is obeyed by the ideal gases. The ideal gases have the elastic collisions between the molecules with no intermolecular attractive forces.

Complete step-by-step answer: To approach this question we have to know the combined gas law. the combined gas law is the following:
\[\dfrac{{{P}_{1}}{{V}_{1}}}{{{T}_{1}}}=\dfrac{{{P}_{2}}{{V}_{2}}}{{{T}_{2}}}\]
So the values given to us in the question are the following:
\[{{P}_{1}}\] is the 1.5 atm
\[{{V}_{1}}\] is the 3.0L
\[{{T}_{1}}\] is the \[{{30}^{o}}C\]= 303K
\[{{T}_{2}}\] is the \[{{20}^{o}}C\]=293K
\[{{P}_{2}}\] is the 2.5 atm
Here we need to calculate the \[{{V}_{2}}\]. So now we will substitute the values in the above formula. We get,
\[\dfrac{1.5\times 3.0}{293}=\dfrac{2.5\times {{V}_{2}}}{303}\]
On simplifying we get,
\[\dfrac{1.5\times 3.0\times 303}{293\times 2.5}={{V}_{2}}\]
On further simplifying we get,
\[{{V}_{2}}=1.867L\]
So the volume if 1.5 atm of the gas at \[{{20}^{o}}C\]the in a 3.0L vessel are heated to at \[{{30}^{o}}C\]a pressure of 2.5 atm will be 1.867L .

Note: The ideal gases which obey the ideal gas law should have elastic collisions with its molecules. The molecules of ideal gas should be in the random motion. The molecules should be in the shape of rigid sphere. The temperature of the gas will be directly proportional to the average kinetic energy of the molecule.