Question

11. Propane (C3Hg) is a fuel commonly used in gas grills.

Answer 1

Answer:

81.71%

Explanation:

One mole of propane contains 3 moles of carbon atoms and 8 moles of hydrogen atoms, as seen from the molecular formula of $C_3H_8$. In order to calculate the percent of carbon in propane by mass, we need to remember that %w/w (or percent mass) formula states that:

$\omega=\frac{m_{component}}{m_{total}}\cdot100\%$

That is, we need to divide the mass of the component of interest by the total mass of the compound and multiply by 100 to obtain the percentage.

For simplicity, let's take 1 mole of propane and find the mass of 1 mole (hence, we'll be finding the molar mass of propane). To do that, we add the 3 molar masses of carbon and 8 molar masses of hydrogen to obtain a total of:

$M_{C_3H_8}=3M_C+8M_H=3\cdot12.011 \frac{g}{mol}+8\cdot1.00784\frac{g}{mol}=44.096 \frac{g}{mol}$

Now that we have the molar mass of propane, we also need to find the total mass of carbon in 1 mole of propane. We know that we have a total of 3 moles of carbon which corresponds to:

$M_C=3\cdot12.011 \frac{g}{mol}=36.033 \frac{g}{mol}$

Dividing the mass of carbon present by the total mass of the compound will yield the mass percentage as defined by the formula we introduced:

$\omega_C=\frac{36.033\frac{g}{mol}}{44.096 \frac{g}{mol}}\cdot 100\%=81.71\%$