Question

How many moles of gas are in a volume of 48.6 L of STP?

Answer 1

Hint: To solve this question, first we have to understand the ideal gas law i.e. PV = nRT where, P is the pressure of the gas and V is the volume.

Complete step by step answer:
1 mole = $6.022\times {{10}^{23}}$ particle or atoms or molecules or electrons or protons etc. The number of the constituent particles of atoms such as molecules or atoms or ions present in a given sample is related with the mass of the substance present in the sample using Avogadro's number. The SI unit of Avogadro’s number is inverse of mole i.e. $mol{{e}^{-1}}$.
- Avogadro’s number is dimensionless. It also helps to relate the molar volume of a substance to the average volume which is occupied by one of the particles.
- At STP the temperature is 273 K and the pressure is 1 atm. The value of the proportionality constant R is equal to 0.0821 $\dfrac{L\times atm}{mol\times K}$
After solving the equation we get:
\[\begin{align}
 & n=\dfrac{PV}{RT} \\
 & n=\dfrac{1atm\times 48.6L}{0.0821\times 273K} \\
 & =2.17mol \\
\end{align}\]

Additional Information :To calculate the number of atoms first we have to calculate the number of moles of the given element if the number of moles is already given, then the mass can easily be calculated. A mole is generally used as a unit for the number of atoms or molecules or particles of a material.

Note: The mole is a measurement or it is the basic unit which helps to calculate the amount of substance present in the given sample. 1 mole of a number is equal to Avogadro’s constant.
- Number of mol is calculated by ratio of given mass to the molar mass.
Number of mol = $\dfrac{\text{given mass}}{molar\text{ mass}}$