Question

Lead nitrate on heating decomposes to give:
$2Pb{\left( {N{O_3}} \right)_2} \to 2PbO + 4N{O_2} + {O_3}$
What is the total volume of gases produced when $13.24{\text{g}}$ of lead nitrate is heated?
All gases are measured at STP.
$\left( {Pb = 207;N = 14;O = 16} \right)$
(A) $2.24$ litres
(B) $1.12$ litres
(C) 2 litres
(D) $1.24$ litres

Answer 1

We need to find the total volume of substance. We need to have a little bit of concept of number of moles for that. First, we shall find the moles of the substance and then use the ideal gas law to find its volume at STP.

Formula used: $n = \dfrac{{{\text{weight of substance}}}}{{{\text{molar mass of substance}}}}$
Here, $n$ is the number of moles.

Complete step by step answer
We already know the given equation.
$2Pb{\left( {N{O_3}} \right)_2} \to 2PbO + 4N{O_2} + {O_3}$
Here, molar mass of ${\text{Pb}}{\left( {{\text{N}}{{\text{O}}_{\text{3}}}} \right)_{\text{2}}} = 207 + 2\left( 4 \right) + 6\left( {16} \right)$
${\text{N}}{{\text{O}}_{\text{2}}}{\text{ and }}{{\text{O}}_{\text{2}}}$ gases are released.
We already know the weight of $Pb{\left( {N{O_3}} \right)_2} = 13.24{\text{g}}$
Number of moles= $\left( {\dfrac{{13.24}}{{33.1}}} \right) = 0.04$
So, $0.04$ moles of $Pb{\left( {N{O_3}} \right)_2}$ gives $\dfrac{{\text{1}}}{{\text{2}}}\left( {\dfrac{{\text{4}}}{{{\text{25}}}}} \right){\text{ moles of N}}{{\text{O}}_{\text{2}}}$
And also produces $\dfrac{{\text{1}}}{{\text{2}}}\left( {\dfrac{{\text{1}}}{{{\text{25}}}}} \right){\text{ moles of }}{{\text{O}}_3}$
Total moles of gases released $= \dfrac{1}{2}\left( {\dfrac{5}{{25}}} \right)$
According to ideal gas law, 1 mole of gas occupies $22.4$ litres.
Total volume of gases= $22.4 \times \left( {\dfrac{5}{{25}}} \right)\dfrac{1}{2} = 2.24{\text{ litres}}$
Thus, the correct option is A.

Additional Information
A mole is defined as the mass of the substance which consists of the equal quantity of basic units. Example atoms in 12 grams are the same as ${12^0}C$ . The basic units can be molecules, atoms or formula units based on the substance. A mole fraction indicates the number of chemical elements. One mole of any substance is equal to the value of $6.023 \times {10^{23}}$ (Avogadro number). It can be used to measure the products obtained from the chemical reaction. The unit is denoted by mol.

Note
Here we are using the concept of stoichiometry. Stoichiometry is a section of chemistry that involves using relationships between reactants and/or products in a chemical reaction to determine desired quantitative data. In Greek, stoikhein means element and metron means measure, so stoichiometry literally translated means the measure of elements.
Thus, to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction. The mass ratios can be calculated by dividing each by the total in the whole reaction.