States of Matter - Result Question 8
####8. A $10 mg$ effervescent tablet containing sodium bicarbonate and oxalic acid releases $0.25 mL$ of $CO _2$ at $T=298.15 K$ and $p=1$ bar. If molar volume of $CO _2$ is $25.0 L$ under such condition, what is the percentage of sodium bicarbonate in each tablet?
[Molar mass of $NaHCO _3=84 g mol^{-1}$ ]
(2019 Main, 11 Jan I)
(a) 8.4
(b) 0.84
(c) 16.8
(d) 33.6
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Solution:
- $2 NaHCO _3+H _2 C _2 O _4 \longrightarrow 2 CO _2+Na _2 C _4 O _4+H _2 O$
$$ 2 mol \quad 1 mol \quad 2 mol $$
$\Rightarrow$ In the reaction, number of mole of $CO _2$ produced.
$$ \begin{aligned} n & =\frac{p V}{R T}=\frac{1 \text { bar } \times 0.25 \times 10^{-3} L}{0.082 L atm K^{-1} mol^{-1} \times 298.15 K} \ & =1.02 \times 10^{-5} mol \end{aligned} $$
Number of mole of $NaHCO _3=\frac{\text { Weight of } NaHCO _3}{\text { Molecular mass of } NaHCO _3}$
$$ \begin{aligned} \therefore \quad w _{NaHCO _3} & =1.02 \times 10^{-5} \times 84 \times 10^{3} mg \ & =0.856 mg \ \Rightarrow NaHCO _3 % & =\frac{0.856}{10} \times 100=8.56 % \end{aligned} $$
