M+ is an unknown metal cation with a +1 charge. A student dissolves the chloride of the unknown meta — Stoichiometry Chemistry Question

STEPS:

1. Calculate the mass of the dry $\text{AgCl}$ precipitate:
Subtract the mass of the filter paper from the mass of the filter paper plus the precipitate:
$$\text{Mass of AgCl} = 2.23\text{ g (filter paper + AgCl)} - 0.80\text{ g (filter paper)} = \mathbf{1.43\text{ g}} \text{}$$
2. Convert the mass of $\text{AgCl}$ to moles:
Use the given molar mass of silver chloride ($143\text{ g/mol}$):
$$\text{Moles of AgCl} = \frac{1.43\text{ g}}{143\text{ g/mol}} = \mathbf{0.010\text{ mol}}$$
3. Determine the moles of the unknown metal chloride ($\text{MCl}$):
The net ionic precipitation reaction is:
$$\text{Ag}^+(aq) + \text{Cl}^-(aq) \rightarrow \text{AgCl}(s) \text{}$$
This stoichiometry indicates a 1:1 mole ratio between $\text{Cl}^-$ ions and $\text{AgCl}$ precipitate. Because the parent metal chloride has the formula $\text{MCl}$, it dissociates to release one mole of chloride ion per mole of salt:
$$\text{MCl}(aq) \rightarrow \text{M}^+(aq) + \text{Cl}^-(aq)$$
Therefore, the moles of $\text{MCl}$ originally dissolved must equal the moles of $\text{AgCl}$ precipitated:
$$\text{Moles of MCl} = 0.010\text{ mol}$$
4. Calculate the molar mass of $\text{MCl}$:
Divide the starting mass of the unknown chloride sample ($0.74\text{ g}$) by the calculated moles:
$$\text{Molar Mass of MCl} = \frac{0.74\text{ g}}{0.010\text{ mol}} = \mathbf{74\text{ g/mol}}$$
5. Determine the atomic mass of the metal ($\text{M}$):
Subtract the molar mass of chlorine ($\approx 35.5\text{ g/mol}$) from the molar mass of the compound:
$$\text{Molar Mass of M} = 74\text{ g/mol} - 35.5\text{ g/mol} = \mathbf{38.5\text{ g/mol}}$$
6. Identify the metal:
Compare the calculated molar mass of the cation ($38.5\text{ g/mol}$) to the molar masses of the alkali metals on the periodic table. Potassium ($\text{K}$) has a molar mass of $39.10\text{ g/mol}$, which is closest to the calculated value. Thus, the unknown metal chloride is potassium chloride ($\text{KCl}$), matching Option B.

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WHY_OTHERS_WRONG:

• A is incorrect: Sodium chloride ($\text{NaCl}$) has a molar mass of $\approx 58.5\text{ g/mol}$. If the sample were $\text{NaCl}$, $0.010\text{ mol}$ of the salt would weigh only $0.58\text{ g}$, which is significantly lower than the actual measured mass of $0.74\text{ g}$.
• C is incorrect: Copper(I) chloride ($\text{CuCl}$) has a molar mass of $\approx 99.0\text{ g/mol}$. If the sample were $\text{CuCl}$, $0.010\text{ mol}$ of the salt would weigh $0.99\text{ g}$, which is much higher than the actual mass of $0.74\text{ g}$.
• D is incorrect: Lithium chloride ($\text{LiCl}$) has a molar mass of $\approx 42.4\text{ g/mol}$. If the sample were $\text{LiCl}$, $0.010\text{ mol}$ of the salt would weigh only $0.42\text{ g}$, which does not match the observed analytical data.