Question

A sample contains 7 wt% CaO and 5 wt% MgO. The molar ratio of CaO to MgO in the sample is ________(Round off to two decimal places)

Hint:

To find the molar ratio of two compounds, calculate the moles of each using their masses and molar masses, then divide the moles of one by the other.

Answer 1

Correct Answer: 0.95

Step 1: Understanding the formula for molar ratio
To calculate the molar ratio of CaO to MgO, we need to use the following formula: \[ {Molar ratio} = \frac{{moles of CaO}}{{moles of MgO}} \] Where:
Moles of a compound can be calculated using the formula: \[ {moles} = \frac{{mass of the compound (g)}}{{molar mass of the compound (g/mol)}} \] Step 2: Calculate the molar masses of CaO and MgO
Molar mass of CaO = \( 40.08 \, {g/mol (for Ca)} + 16.00 \, {g/mol (for O)} = 56.08 \, {g/mol} \)
Molar mass of MgO = \( 24.31 \, {g/mol (for Mg)} + 16.00 \, {g/mol (for O)} = 40.31 \, {g/mol} \)
Step 3: Calculate the moles of CaO and MgO in 100 g of the sample
Given the mass percentages:
Mass of CaO = 7 g (since the sample is 100 g)
Mass of MgO = 5 g
Now, calculate the moles:
Moles of CaO = \( \frac{7}{56.08} \)
Moles of MgO = \( \frac{5}{40.31} \)
Step 4: Calculate the molar ratio
Using the formula for molar ratio: \[ {Molar ratio} = \frac{\frac{7}{56.08}}{\frac{5}{40.31}} \] \[ {Molar ratio} = \frac{7 \times 40.31}{5 \times 56.08} \approx \frac{281.17}{280.4} \approx 1.00 \] Step 5: Final answer
The molar ratio of CaO to MgO in the sample is approximately \(1.00\).