To determine the correct formula of the gaseous metallic chloride MClx, we need to analyze the given information step by step. ### Step 1: Understanding the Mass Percentage We know that the metallic chloride consists of 20.22% of metal (M) by mass. This means that in a sample of the compound, 20.22 grams of the total mass is due to the metal M, and the remaining mass is due to chlorine (Cl). ### Step 2: Setting Up the Mass Relationship Let’s assume we have 100 grams of the compound MClx. In this case: - Mass of M = 20.22 grams - Mass of Cl = 100 grams - 20.22 grams = 79.78 grams ### Step 3: Calculating Moles of M and Cl Next, we need to convert these masses into moles using the molar masses provided: - Molar mass of M = 27 g/mol - Molar mass of Cl = 35.5 g/mol **Calculating moles of M:** \[ \text{Moles of M} = \frac{\text{Mass of M}}{\text{Molar mass of M}} = \frac{20.22 \text{ g}}{27 \text{ g/mol}} \approx 0.749 \text{ moles} \] **Calculating moles of Cl:** \[ \text{Moles of Cl} = \frac{\text{Mass of Cl}}{\text{Molar mass of Cl}} = \frac{79.78 \text{ g}}{35.5 \text{ g/mol}} \approx 2.25 \text{ moles} \] ### Step 4: Finding the Mole Ratio Now, we need to find the simplest whole number ratio of moles of M to moles of Cl. We do this by dividing both values by the smaller number of moles (which is approximately 0.749). **Calculating the ratio:** \[ \text{Ratio of M} = \frac{0.749}{0.749} = 1 \] \[ \text{Ratio of Cl} = \frac{2.25}{0.749} \approx 3 \] This gives us a ratio of 1:3 for M:Cl. ### Step 5: Writing the Empirical Formula From the mole ratio, we can deduce that for every 1 atom of M, there are 3 atoms of Cl. Therefore, the empirical formula of the compound is: \[ \text{MCl}_3 \] ### Step 6: Evaluating the Options Now, let’s evaluate the options provided: - **A. MCl**: This would imply a 1:1 ratio of M to Cl, which does not match our findings. - **B. MCl2**: This would imply a 1:2 ratio of M to Cl, which is also incorrect based on our calculations. - **C. MCl3**: This matches our calculated ratio of 1:3, making it the correct answer. - **D. M2Cl6**: This is equivalent to MCl3 (since 2:6 simplifies to 1:3), but it is not the simplest form of the formula. ### Conclusion The correct answer is **C. MCl3** because it accurately reflects the mole ratio derived from the mass percentage of the components in the compound. ### Revision Summary - The mass percentage of M was used to find the mass of Cl in the compound. - Moles of M and Cl were calculated using their respective molar masses. - The simplest mole ratio of M to Cl was determined to be 1:3. - The empirical formula derived from the mole ratio is MCl3, confirming option C as correct.