Question

Fungal laccase, a blue protein found in wood-rotting fungi, is 0.390% Cu by mass. If a fungallaccase molecule contains four copper atoms, what is the molar mass of fungal laccase?

Short answer

The molar mass of fungal laccase is$6.52\times {10}^4\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.$.

Step-by-step solution

Calculating of mass of copper in 1 mole

The molecule of fungal laccase contains 4 copper atoms which means 1 mole has copper 4 moles. The molar mass of copper is 63.55 g/mol. On multiplying the mole number of copper atoms to find amount of copper present in 1 mole.

$4\mathrm{mol}\mathrm{Cu}\times \frac{63.55\mathrm{gCu}}{1\mathrm{mol}\mathrm{Cu}}=254.2\mathrm{g}\mathrm{Cu}$

The copper mass in 1 mole is 254.2 g Cu.

Expression of copper’s mass percentage

The expression of copper’s mass percentage in fungal laccase are denoted as,

$\mathrm{Mass}\mathrm{Percent}\mathrm{of}\mathrm{Cu}=\frac{\mathrm{mass}\mathrm{of}\mathrm{Cu}\mathrm{in}1\mathrm{m}\mathrm{ol}\mathrm{fungal}\mathrm{laccase}}{\mathrm{mass}\mathrm{of}1\mathrm{m}\mathrm{ol}\mathrm{fungol}\mathrm{laccase}}\times 100$

Mass percentage of copper in fungal laccase are 0.39 %. Copper’s mass in 1 mole is 254.2 g Cu.

Expression of mass percentage of fungal laccase

On substituting the copper’s mass and mass percentage to find molar mass,

$\begin{array}{rcl}\mathrm{Mass}\mathrm{Percent}\mathrm{of}\mathrm{Cu}& =& \frac{\mathrm{mass}\mathrm{of}\mathrm{Cu}\mathrm{in}1\mathrm{m}\mathrm{ol}\mathrm{fungal}\mathrm{laccase}}{\mathrm{mass}\mathrm{of}1\mathrm{mol}\mathrm{fungol}\mathrm{laccase}}\times 100\\ 0.39\mathrm{percent}& =& \frac{254.2}{\mathrm{mass}\mathrm{of}1\mathrm{mol}\mathrm{fungol}\mathrm{laccase}}\times 100\\ \mathrm{Mass}\mathrm{of}1\mathrm{mol}\mathrm{fungol}\mathrm{laccase}& =& \frac{\left(254.2\mathrm{g}\right)}{\left(0.39\mathrm{Percent}\right)}\times 100\\ & =& 6.52\times {10}^4\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.\end{array}$