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

Step 1: Understanding the Formula for Molar Ratio
To calculate the molar ratio of CaO to MgO, we use the following formula:

\[ \text{Molar ratio} = \frac{\text{moles of CaO}}{\text{moles of MgO}} \]
Where:
Moles of a compound can be calculated using the formula:

\[ \text{moles} = \frac{\text{mass of the compound (g)}}{\text{molar mass of the compound (g/mol)}} \]

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:

\[ \text{Molar ratio} = \frac{\frac{7}{56.08}}{\frac{5}{40.31}} \]
\[ \text{Molar ratio} = \frac{7 \times 40.31}{5 \times 56.08} \approx \frac{281.17}{280.4} \approx 1.00 \]

Step 5: Final Answer
The molar ratio of CaO to MgO in the sample is approximately 1.00.