Question

\(A + 2B \longrightarrow AB_2\)
\(36.0\,\text{g}\) of \(A\) (Molar mass \(= 60\,\text{g mol}^{-1}\)) and \(56.0\,\text{g}\) of \(B\) (Molar mass \(= 80\,\text{g mol}^{-1}\)) are allowed to react. Which of the following statements are correct?
[A.] \(A\) is the limiting reagent.
[B.] \(77.0\,\text{g}\) of \(AB_2\) is formed.
[C.] Molar mass of \(AB_2\) is \(140\,\text{g mol}^{-1}\).
[D.] \(15.0\,\text{g}\) of \(A\) is left unreacted after completion of reaction. Choose the correct answer from the options given below:

• A. A and B only
• B. A and C only
• C. B and D only
• D. C and D only

Hint:

Always compare mole ratios with stoichiometric coefficients to identify the limiting reagent.

Answer 1

The Correct Option is C

Consider the chemical reaction:

\[ A + 2B \longrightarrow AB_2 \]

Given:

• Mass of \(A = 36.0\,\text{g}\)
• Molar mass of \(A = 60.0\,\text{g mol}^{-1}\)
• Mass of \(B = 56.0\,\text{g}\)
• Molar mass of \(B = 80.0\,\text{g mol}^{-1}\)

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Step 1: Calculate moles of reactants

Moles of \(A\):

\[ n_A = \frac{36.0}{60} = 0.6~\text{mol} \]

Moles of \(B\):

\[ n_B = \frac{56.0}{80} = 0.7~\text{mol} \]

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Step 2: Identify the limiting reagent

According to the balanced equation, 1 mole of \(A\) requires 2 moles of \(B\).

Moles of \(B\) required for 0.6 mol of \(A\):

\[ 0.6 \times 2 = 1.2~\text{mol of } B \]

Since only 0.7 mol of \(B\) is available, \(B\) is the limiting reagent.

Conclusion for Statement (A): Incorrect.

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Step 3: Amount of product formed

From stoichiometry:

\[ \text{Moles of } AB_2 = \frac{0.7}{2} = 0.35~\text{mol} \]

Molar mass of \(AB_2\):

\[ 60 + 2(80) = 220~\text{g mol}^{-1} \]

Mass of \(AB_2\) formed:

\[ 0.35 \times 220 = 77.0~\text{g} \]

Conclusion for Statement (B): Correct.

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Step 4: Check molar mass statement

Calculated molar mass of \(AB_2 = 220~\text{g mol}^{-1}\), not 140.

Conclusion for Statement (C): Incorrect.

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Step 5: Unreacted amount of \(A\)

Moles of \(A\) reacted:

\[ \frac{0.7}{2} = 0.35~\text{mol} \]

Moles of \(A\) left:

\[ 0.6 - 0.35 = 0.25~\text{mol} \]

Mass of unreacted \(A\):

\[ 0.25 \times 60 = 15.0~\text{g} \]

Conclusion for Statement (D): Correct.

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Final Answer

\[ \boxed{\text{B and D only}} \]