Question

How many moles of a pure gas are in a 30 liter scuba canister if the temperature of the canister is ${{27}^{0}}C$ and the pressure is 0.4 atmospheres?

Answer 1

Hint: Use the formula of ideal gas equation and substitute the given data in the formula; then calculate and find the number of moles. More the number of pressure and volume and lesser the temperature, more will be the number of moles.

Complete step-by-step answer: In order to answer the question, we need to know about moles and molar mass. Now, matter is made up of atoms, and as matter has mass, then the atoms should have an individual mass. Molar mass of an element or compound is the mass which houses $6\times {{10}^{23}}$ particles. For, example, the hydrogen molecule has a molar mass of 2 grams. This means 2 grams of hydrogen contains $6\times {{10}^{23}}$atoms, and this number is also called the Avogadro’s number.
Number of moles of an element or a compound is the ratio of its given mass taken by the user, to its molar mass. More is the number of moles, more is the concentration of the substance. Now, let us come to the question.
We have been asked about the number of moles in a pure gas, and parameters like temperature, pressure and volume have been given to us. So, we can find the unknown variable, in this case, the number of moles, by using the ideal gas equation. The ideal gas equation can be written as:
     \[PV=nRT\]
Here, P means pressure, V means volume, n is the number of moles, R is the universal gas constant and T stands for temperature. So, now let us substitute the given data in the equation and find the number of moles. On rearranging, we get the number of moles as:
\[
  n=\dfrac{PV}{RT} \\
 \Rightarrow n=\dfrac{0.4\times 30}{0.0821\times 300}=0.487mol \\
\]
So, we obtain the number of moles of the gas as 0.487 mol which is the required answer for the question.

Note: It is to be noted that we have taken the value of universal gas constant to be $0.0821\,L\,atm\,{{K}^{-1}}mo{{l}^{-1}}$. Also, the temperature in Celsius has been converted to kelvin, for convenience.