Magnesium on heating reacts vigorously with element X to produce compound Y. An aqueous solution of Y, when treated with aqueous silver nitrate , gives a white precipitate that is readily soluble in dilute aqueous ammonia. What is the minium mass of X that is needed to react completely with 4.05g of magnesium

Options

A. 11.83g
B. 5.92g
C. 5.33g
D. 2.67g

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript and perform the necessary calculations.

### Step 1: Identify the Reaction
Magnesium (Mg) reacts with element X to produce compound Y. Given that the aqueous solution of Y reacts with silver nitrate (AgNO3) to form a white precipitate that is soluble in dilute ammonia, we can deduce that Y contains chlorine (Cl). The white precipitate formed is silver chloride (AgCl).

### Step 2: Determine Element X
Since Y must contain chlorine, we can conclude that element X is chlorine (Cl). Therefore, the reaction can be written as:
\[ \text{Mg} + \text{Cl}_2 \rightarrow \text{MgCl}_2 \]

### Step 3: Calculate Moles of Magnesium
We are given the mass of magnesium:
- Mass of magnesium (Mg) = 4.05 g

To find the number of moles of magnesium, we use the formula:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \]

The molar mass of magnesium (Mg) is approximately 24.31 g/mol. Thus:
\[ \text{Number of moles of Mg} = \frac{4.05 \, \text{g}}{24.31 \, \text{g/mol}} \approx 0.1663 \, \text{moles} \]

### Step 4: Determine Moles of Chlorine Required
From the balanced reaction, we see that 1 mole of magnesium reacts with 1 mole of chlorine gas (Cl2). Therefore, the number of moles of Cl2 required is equal to the number of moles of Mg:
\[ \text{Moles of Cl}_2 = 0.1663 \, \text{moles} \]

### Step 5: Calculate Mass of Chlorine
Now, we need to calculate the mass of chlorine gas (Cl2) required. The molar mass of Cl2 is approximately 70.90 g/mol. We can use the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]

Thus:
\[ \text{Mass of Cl}_2 = 0.1663 \, \text{moles} \times 70.90 \, \text{g/mol} \approx 11.82 \, \text{g} \]

### Step 6: Round to Appropriate Significant Figures
Rounding the mass of chlorine to three significant figures gives us:
\[ \text{Mass of Cl}_2 \approx 11.83 \, \text{g} \]

### Conclusion
The minimum mass of element X (chlorine) needed to react completely with 4.05 g of magnesium is approximately **11.83 g**.