A mass of 8.4 g of pure sodium hydrogen carbonate was completely converted to sodium carbonate, water and carbon dioxide by the action of heat - Leaving Cert Chemistry - Question b - 2013

From the balanced chemical equation, we see that 2 moles of NaHCO₃ produce 1 mole of H₂O. Therefore, if 0.1 moles of NaHCO₃ are used, the amount of H₂O produced can be calculated as follows:

$\text{Moles of } H_2O = 0.1 \text{ moles NaHCO₃} \times \frac{1 \text{ mole } H_2O}{2 \text{ moles } NaHCO₃} = 0.05 \text{ moles } H_2O$

Now, we can find the mass of water using:

$m = n \cdot M$

The molar mass of water (H₂O) is:

• H: 1 g/mol \times 2 = 2 g/mol
• O: 16 g/mol

Thus,

$M_{H_2O} = 2 + 16 = 18 \text{ g/mol}$

Now, the mass of water produced is:

$m = 0.05 \text{ moles} \times 18 \text{ g/mol} = 0.9 \text{ g}$

From the equation, 2 moles of NaHCO₃ produce 1 mole of CO₂. Therefore, the amount of CO₂ produced is:

$\text{Moles of } CO_2 = 0.1 \text{ moles NaHCO₃} \times \frac{1 \text{ mole } CO_2}{2 \text{ moles } NaHCO₃} = 0.05 \text{ moles } CO_2$

At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.4 liters. Thus, the volume of CO₂ produced can be calculated as:

$\text{Volume} = n \cdot 22.4 \text{ L}$

The volume of CO₂ is:

$\text{Volume} = 0.05 \text{ moles} \times 22.4 \text{ L/mol} = 1.12 \text{ L}$

To find the number of molecules of CO₂, we use Avogadro's number, which states that 1 mole of a substance contains approximately $6.022 \times 10^{23}$ molecules. Given that we have 0.05 moles of CO₂, the number of molecules is:

$\text{Number of molecules} = 0.05 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol}$

Calculating this gives:

$\text{Number of molecules} = 3.011 \times 10^{22} \text{ molecules} \approx 3 \times 10^{22} \text{ molecules}$