Question

Chlorophyll, the substance responsible for the green color of leaves, has one magnesium atom per chlorophyll molecule and contains \(2.72 \%\) magnesium by mass. What is the molar mass of chlorophyll?

Short answer

Answer: The molar mass of chlorophyll is approximately 892.86 g/mol.

Step-by-step solution

Find the mass of magnesium in a given mass of chlorophyll

Since chlorophyll contains \(2.72 \%\) magnesium by mass, we can find the mass of magnesium in a given mass of chlorophyll. Let's consider a \(100 g\) sample of chlorophyll. In that sample, the mass of magnesium would be: Mass of magnesium \( = 2.72 \% \times 100 g = 2.72 g\)

Determine the moles of magnesium from its mass

In order to find the molar mass of chlorophyll, we need to relate the amount of magnesium in moles to the amount of chlorine in moles. First, we need to convert the mass of magnesium to moles. The atomic weight of magnesium is approximately \(24.3 g/mol\). We can use this to find the number of moles (n) of magnesium: \(n_{Mg} = \frac{\text{mass of magnesium}}{ \text{atomic weight of magnesium}}\) \(n_{Mg} = \frac{2.72 g}{24.3 g/mol} = 0.112 moles \, of \, Mg\)

Determine the moles of chlorophyll in the sample

There is one magnesium atom per chlorophyll molecule, and we have calculated the moles of magnesium in our sample to be \(0.112 moles\). Then, the moles of chlorophyll in the sample is also: \(n_{Chlorophyll} = 0.112 moles \, of \, Chlorophyll\) Now we can relate the mass of chlorophyll to the number of moles we calculated.

Calculate the molar mass of chlorophyll

From step 1, we have the mass of chlorophyll, \(100 g\), and from step 3 we know the number of moles, \(0.112 moles\). Now we can calculate the molar mass of chlorophyll using the formula: Molar mass of chlorophyll \( = \frac{\text{mass of chlorophyll}}{ \text{moles of chlorophyll}}\) Molar mass of chlorophyll \( = \frac{100 g}{0.112 moles} \approx 892.86 g/mol\) Hence, the molar mass of chlorophyll is approximately \(892.86 g/mol\).