Question

The mineral formula of orthopyroxene calculated on 6 Oxygen atom basis is (Mg1.2Fe0.8)Si2O6. The weight percentage of MgO in the chemical composition of orthopyroxene is ............. (Round off to one decimal place)

Hint:

To calculate the weight percentage of an element in a mineral, find the mass of the element, then divide it by the total molar mass of the mineral and multiply by 100.

Answer 1

Step 1: Write the formula of orthopyroxene.
The given formula is: \[ (Mg_{1.2}Fe_{0.8})Si_2O_6 \] Step 2: Calculate the molar mass of MgO.
The molecular weight of MgO is: \[ \text{MgO} = 24.305 + 16.00 = 40.305 \, \text{g/mol} \] Step 3: Determine the moles of MgO in the formula.
From the formula \( (Mg_{1.2}Fe_{0.8})Si_2O_6 \), we see that there are 1.2 moles of Mg in the formula. Thus, the mass of Mg in the formula is: \[ \text{Mg mass} = 1.2 \times 24.305 = 29.166 \, \text{g} \] Step 4: Calculate the total molar mass of the orthopyroxene formula.
The molar mass of \( (Mg_{1.2}Fe_{0.8})Si_2O_6 \) is calculated as follows: \[ \text{Molar mass of orthopyroxene} = (1.2 \times 24.305) + (0.8 \times 55.845) + (2 \times 28.085) + (6 \times 16.00) \] \[ \text{Molar mass of orthopyroxene} = 29.166 + 44.676 + 56.170 + 96.000 = 225.012 \, \text{g/mol} \] Step 5: Calculate the weight percentage of MgO.
The weight percentage of MgO is given by: \[ \text{Weight percentage of MgO} = \frac{\text{Mass of Mg}}{\text{Molar mass of orthopyroxene}} \times 100 \] \[ \text{Weight percentage of MgO} = \frac{29.166}{225.012} \times 100 = 12.98 % \approx 13.0% \] Final Answer: \[ \boxed{13.0} \]