a. To calculate the molar mass (Mr) of lead dioxide (PbO₂), we add the molar masses of lead (Pb) and oxygen (O).
- Molar mass of Pb = 207.2 g/mol
- Molar mass of O = 16.0 g/mol
Since there are 2 oxygen atoms in PbO₂, we have:
\[ \text{Mr of PbO₂} = \text{Mr of Pb} + 2 \times \text{Mr of O} \] \[ \text{Mr of PbO₂} = 207.2 + 2 \times 16.0 \] \[ \text{Mr of PbO₂} = 207.2 + 32.0 = 239.2 \text{ g/mol} \]
Answer: The Mr of PbO₂ is 239.2 g/mol.
b. i. To calculate the number of moles of lead dioxide used:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{478 \text{ g}}{239.2 \text{ g/mol}} \]
\[ \text{Number of moles of PbO₂} = 2.00 \text{ moles} , (\text{rounded to 2 decimal places}) \]
Answer: The number of moles of lead dioxide used is 2.00 moles.
ii. According to the balanced equation, 1 mole of PbO₂ produces 1 mole of Pb. Therefore, the number of moles of lead produced is equal to the number of moles of lead dioxide used.
\[ \text{Number of moles of Pb} = \text{Number of moles of PbO₂} = 2.00 \text{ moles} \]
Answer: The number of moles of lead produced is 2.00 moles.
iii. To find the mass of lead produced:
\[ \text{Mass} = \text{Number of moles} \times \text{molar mass of Pb} \] \[ \text{Mass of Pb} = 2.00 \text{ moles} \times 207.2 \text{ g/mol} = 414.4 \text{ g} \]
Answer: The mass of lead produced is 414.4 g.
c. To calculate the mass of hydrogen needed to produce 20.7 g of Pb, we first need to find the number of moles of Pb produced.
i. Calculate the number of moles of Pb:
\[ \text{Number of moles of Pb} = \frac{\text{mass}}{\text{molar mass}} = \frac{20.7 \text{ g}}{207.2 \text{ g/mol}} \approx 0.1 \text{ moles} , (\text{rounded to 1 decimal place}) \]
ii. From the balanced equation, 1 mole of PbO₂ reacts with 2 moles of H₂ to produce 1 mole of Pb. Therefore, the number of moles of hydrogen needed is:
\[ \text{Number of moles of H₂} = 2 \times \text{Number of moles of Pb} = 2 \times 0.1 = 0.2 \text{ moles} \]
iii. Now, calculate the mass of hydrogen needed:
\[ \text{Molar mass of H₂} = 2 \times \text{molar mass of H} = 2 \times 1.0 = 2.0 \text{ g/mol} \]
Now we can find the mass of hydrogen needed:
\[ \text{Mass of H₂} = \text{Number of moles of H₂} \times \text{molar mass of H₂} = 0.2 \text{ moles} \times 2.0 \text{ g/mol} = 0.4 \text{ g} \]
Answer: The mass of hydrogen needed to make 20.7 g of Pb is 0.4 g.