Question

For an ideal gas, how do you calculate the pressure in atm if $8.25\times {{10}^{-2}}\,mol$ occupies 174mL at ${{215}^{0}}C$?

Answer 1

Hint: Since all the parameters except the pressure are given in the question, we use the equation of ideal gas to find out the required pressure.

Complete answer:
In order to answer our question, we need to use the concept of the ideal gas equation. Ideal gas equation is an equation which is followed by the ideal gases. A gas that would obey Boyle's and Charles Law under all the conditions of pressure and temperature is called an ideal gas. The ideal gas equation is shown as:
\[PV=nRT\]
This is the ideal gas equation as it is obeyed by the hypothetical gases called ideal gases under all conditions of temperature and pressure. However there is no gas that is perfectly ideal. But the gases may show nearly ideal behaviour under the conditions of low pressure and high temperature and are called real gases.
R(Proportionality constant):
(1) It is a gas constant
(2) It is the same for all the gases.
Therefore it is also called universal gas constant. The value of 'R' depends upon the units in which pressure and volume are taken.
Now, let us come to the question. Except for the pressure, we have been provided with every other value in the question. So, we will substitute the values in the ideal gas equation and find the pressure which is:
\[\begin{align}
  & P=\dfrac{8.25\times {{10}^{-2}}\times 0.0821\times 488}{0.174} \\
 & P=\dfrac{330.53}{17.4}\approx 19 \\
\end{align}\]
So, we get the value of the pressure from the values given in the question as 19 atm, which is the required answer for our question.

Note:
The Boyle’s and the Charles Law can be combined to give a relationship between the variables P, V and T, which is called the combined gas equation and it is represented by:
\[\dfrac{{{P}_{1}}{{V}_{1}}}{{{T}_{1}}}=\dfrac{{{P}_{2}}{{V}_{2}}}{{{T}_{2}}}\]