Question

when baking soda (solid sodium bicarbonate or sodium hydrogen carbonate, nahco₃) is heated, it releases carbon dioxide gas which is responsible for the rising of cookies, donuts, and bread.
part 1 of 2
write a balanced equation for the decomposition of the compound (one of three products is solid sodium carbonate, na₂co₃).
part 2 of 2
calculate the mass of nahco₃ required to produce 21.8 g of co₂. round your answer to 3 significant digits.

Explanation:

Step1: Write the balanced chemical equation

The decomposition of sodium bicarbonate ($NaHCO_3$) is $2NaHCO_3(s)
ightarrow Na_2CO_3(s)+H_2O(g)+CO_2(g)$

Step2: Calculate molar masses

The molar mass of $CO_2$ ($M_{CO_2}$): $M_{CO_2}=12.01 + 2\times16.00=44.01\ g/mol$
The molar mass of $NaHCO_3$ ($M_{NaHCO_3}$): $M_{NaHCO_3}=22.99+1.01 + 12.01+3\times16.00 = 84.01\ g/mol$

Step3: Calculate moles of $CO_2$

Given mass of $CO_2$ is $m_{CO_2}=21.8\ g$. Moles of $CO_2$, $n_{CO_2}=\frac{m_{CO_2}}{M_{CO_2}}=\frac{21.8\ g}{44.01\ g/mol}\approx0.495\ mol$

Step4: Determine moles of $NaHCO_3$ from mole - ratio

From the balanced equation, the mole - ratio of $NaHCO_3$ to $CO_2$ is $2:1$. So moles of $NaHCO_3$, $n_{NaHCO_3}=2\times n_{CO_2}=2\times0.495\ mol = 0.99\ mol$

Step5: Calculate mass of $NaHCO_3$

Mass of $NaHCO_3$, $m_{NaHCO_3}=n_{NaHCO_3}\times M_{NaHCO_3}=0.99\ mol\times84.01\ g/mol\approx83.2\ g$

Answer:

$83.2\ g$