Question

When a sample of baking soda was strongly ignited in a crucible, it suffered a loss in weight of $3.1$g. the mass of baking soda is:
A. $16.8\,{\text{g}}$
B.$8.4\,{\text{g}}$
C.$11.6\,{\text{g}}$
D.$4.2\,{\text{g}}$

Answer 1

We will write the balanced equation for the decomposition of the baking soda. Then determine the amount of baking soda and product. By comparing the mass lost with the amount of baking soda required from balanced reaction we can determine the mass of baking soda required for the $3.1$g loss in weight.

Complete answer:
The chemical formula of baking powder is ${\text{NaHC}}{{\text{O}}_{\text{3}}}$.
The decomposition reaction of sodium hydrogen carbonate is as follows:
${\text{2NaHC}}{{\text{O}}_{\text{3}}}\,\mathop \to \limits^\Delta {\text{N}}{{\text{a}}_{\text{2}}}{\text{C}}{{\text{O}}_{\text{3}}}\,{\text{ + }}\,{\text{C}}{{\text{O}}_{\text{2}}}\, + \,{{\text{H}}_2}{\text{O}}$
The decomposition of sodium hydrogen carbonate on heating produces sodium carbonate, carbon dioxide, and water.

We will determine the mass of sodium hydrogen carbonate, water and carbon dioxide by using mole formula as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
Molar mass of sodium hydrogen carbonate is $84\,{\text{g/mol}}$.
So, the mass of two moles of sodium hydrogen carbonate is,
${\text{2}}\,{\text{mol}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{84\,{\text{g/mol}}}}$
$\Rightarrow {\text{mass}} = \,{\text{2}}\,{\text{mol}}\,\, \times \,84\,{\text{g/mol}}\,$
$\Rightarrow{\text{mass}} = \,168\,{\text{g/mol}}\,$
Molar mass of water is $18\,{\text{g/mol}}$.
So, the mass of one moles of water is $18\,{\text{g/mol}}$.
Molar mass of carbon dioxide is $44\,{\text{g/mol}}$.
So, the mass of one moles of carbon dioxide is $44\,{\text{g/mol}}$.
On heating sodium hydrogen carbonate mass lost in form of carbon dioxide and water so, the total mass of carbon dioxide and water is,
${\text{mass}}\,\,{\text{lost}}\,{\text{ = }}\,\,\,{\text{44}}\,{\text{g/mol + }}\,18\,{\text{g/mol}}$
$\Rightarrow{\text{mass}}\,\,{\text{lost}}\,{\text{ = }}\,\,\,{\text{62}}\,{\text{g}}$
So, we can say on heating $168\,{\text{g}}$ of sodium hydrogen carbonate the mass lost is ${\text{62}}\,{\text{g}}$. So, the mass of sodium hydrogen carbonate require to lose of $\Rightarrow 3.1$g will be,
${\text{62}}\,{\text{g}}$ mass loss = $168\,{\text{g}}$ of sodium hydrogen carbonate
$3.1$g mass loss = $8.4\,{\text{g}}$ of sodium hydrogen carbonate
So, the mass of baking soda is $8.4\,{\text{g}}$.

**Therefore, option (B) $8.4\,{\text{g}}$ is correct.

Note:**
For the stoichiometric calculation a balanced chemical equation is required. Baking soda is mainly a mixture of bases such as carbonate or bicarbonate and weak acid. When the baking powder is heated with the food, sodium hydrogen carbonate decomposes and releases the carbon dioxide gas in the form of bubbles. This gas increases the volume of the dough. So, the baking powder is used to give the volume to the dough.