Question

A diamondiferous lamproite is ultrapotassic and has a molar \( \text{K}_2\text{O}/\text{Na}_2\text{O} \) ratio of 11. If the \( \text{Na}_2\text{O} \) content of the rock is 0.62 wt%, the \( \text{K}_2\text{O} \) content is .......... wt% (answer in one decimal place; molecular weight of \( \text{Na}_2\text{O} = 61.98 \), and \( \text{K}_2\text{O} = 94.20 \)).

Hint:

Use the molar ratio to convert between the moles of two components, and then convert moles to weight percent using the molar masses.

Answer 1

Correct Answer: 10.3 - 10.5

Step 1: Understand the molar ratio. 
The molar ratio \( \text{K}_2\text{O}/\text{Na}_2\text{O} \) is given as 11. This means: \[ \frac{\text{Moles of } \text{K}_2\text{O}}{\text{Moles of } \text{Na}_2\text{O}} = 11 \] We are given that the \( \text{Na}_2\text{O} \) content in the rock is 0.62 wt%. Our goal is to calculate the weight percent of \( \text{K}_2\text{O} \).

Step 2: Use the molar ratio to calculate the weight percent of \( \text{K}_2\text{O} \). 
First, we need to convert the weight percent of \( \text{Na}_2\text{O} \) to moles, then use the molar ratio to find the moles of \( \text{K}_2\text{O} \). 1. Moles of \( \text{Na}_2\text{O} \) in 0.62 wt%: The mass of \( \text{Na}_2\text{O} \) is 0.62 g per 100 g of rock. The moles of \( \text{Na}_2\text{O} \) is: \[ \text{Moles of Na}_2\text{O} = \frac{0.62 \, \text{g}}{61.98 \, \text{g/mol}} = 0.01 \, \text{mol} \] 2. Moles of \( \text{K}_2\text{O} \): From the molar ratio \( \frac{\text{K}_2\text{O}}{\text{Na}_2\text{O}} = 11 \), the moles of \( \text{K}_2\text{O} \) is: \[ \text{Moles of K}_2\text{O} = 11 \times 0.01 = 0.11 \, \text{mol} \] 3. Convert moles of \( \text{K}_2\text{O} \) to weight percent: The mass of \( \text{K}_2\text{O} \) is: \[ \text{Mass of K}_2\text{O} = 0.11 \, \text{mol} \times 94.20 \, \text{g/mol} = 10.362 \, \text{g} \] 

Thus, the weight percent of \( \text{K}_2\text{O} \) in 100 g of rock is: \[ \text{Weight \% of K}_2\text{O} = \frac{10.362 \, \text{g}}{100 \, \text{g}} \times 100 = 10.4\% \]

Step 3: Conclusion. 
The weight percent of \( \text{K}_2\text{O} \) is 10.4 wt%.