Step-by-Step Solution

The problem asks for the amount of the final product S in grams, starting from 16 moles of compound X (Phenol). The reaction sequence and yield for each step are given.

Step 1: Identify the reactants and products in each step.

1. X → P: The starting material X is phenol ($C_6H_5OH$). The reagents are $NaOH$ followed by $CH_3Br$. This is a Williamson Ether Synthesis. Phenol, being acidic, reacts with $NaOH$ to form sodium phenoxide ($C_6H_5O^-Na^+$), which then acts as a nucleophile and attacks $CH_3Br$ to form an ether.

   • Product P is Anisole (methoxybenzene), $C_6H_5OCH_3$. The yield is 80%.

2. P → Q: The reagent is $Br_2$ in the presence of $Fe$ (a Lewis acid catalyst, forming $FeBr_3$ in situ). This is an electrophilic aromatic substitution (bromination). The methoxy group ($-OCH_3$) is a strongly activating, ortho-para directing group. The major product is the para isomer due to less steric hindrance.

   • Product Q is p-Bromoanisole (4-bromoanisole), $p-Br-C_6H_4-OCH_3$. The yield is 75%.

3. Q → R: The reagents are $Mg$ and dry ether. This reaction forms a Grignard reagent.

   • Product R is p-methoxyphenylmagnesium bromide, $p-CH_3O-C_6H_4-MgBr$. The yield is 90%.

4. R → S: The reagents are acetaldehyde ($CH_3CHO$) followed by an acidic workup ($H_3O^+$). The Grignard reagent (R) attacks the electrophilic carbonyl carbon of acetaldehyde, followed by protonation of the resulting alkoxide.

   • Product S is 1-(4-methoxyphenyl)ethanol, $p-CH_3O-C_6H_4-CH(OH)CH_3$. The yield is 85%.

Step 2: Calculate the molar mass of the final product S.

• The chemical formula for S, 1-(4-methoxyphenyl)ethanol, is $C_9H_{12}O_2$.
• Using the given atomic masses (C=12, H=1, O=16): $\text{Molar Mass of S} = (9 \times 12) + (12 \times 1) + (2 \times 16) = 108 + 12 + 32 = 152 \text{ g/mol}$

Step 3: Calculate the overall molar yield and the moles of S produced.

• The initial amount of X is 16 moles.
• The yields are applied sequentially. The overall yield is the product of the individual yields. $\text{Overall Yield} = 0.80 \times 0.75 \times 0.90 \times 0.85$ $\text{Overall Yield} = 0.60 \times 0.90 \times 0.85 = 0.54 \times 0.85 = 0.459$
• The moles of S produced are calculated by multiplying the initial moles of X by the overall yield. $\text{Moles of S} = \text{Initial Moles of X} \times \text{Overall Yield}$ $\text{Moles of S} = 16 \text{ mol} \times 0.459 = 7.344 \text{ mol}$

Step 4: Calculate the mass of S produced.

• The mass of S is the product of its moles and molar mass. $\text{Mass of S} = \text{Moles of S} \times \text{Molar Mass of S}$ $\text{Mass of S} = 7.344 \text{ mol} \times 152 \text{ g/mol} = 1116.288 \text{ g}$

Step 5: Final Answer.

The question asks for the amount in grams, and this is an integer-type question, so we round the result to the nearest integer.

$\text{Amount of S} = 1116 \text{ g}$

Comparison with Stored Answer

The calculated answer based on the problem statement is 1116 g. The stored correct answer is 175. There is a significant discrepancy.

The calculation has been thoroughly checked. The source of the discrepancy is likely a typo in the problem statement. If we assume the initial amount of X was 2.5 moles instead of 16 moles, the calculation would be:

• Moles of S = $2.5 \text{ mol} \times 0.459 = 1.1475 \text{ mol}$
• Mass of S = $1.1475 \text{ mol} \times 152 \text{ g/mol} = 174.42 \text{ g}$

This value (174.42 g) is very close to the stored answer of 175 g, with the small difference likely due to rounding in the given yield percentages. However, based on the question as written (with 16 moles of X), the correct answer is 1116 g.