MCQEasyJEE 2023Mole Concept

JEE Chemistry 2023 Question with Solution

The number of molecules and moles in 2.8375litres2.8375 \, \text{litres} of O2O_2 at STP are respectively:

  • A

    7.527×10227.527 \times 10^{22} and 0.125mol0.125 \, \text{mol}

  • B

    1.505×10231.505 \times 10^{23} and 0.250mol0.250 \, \text{mol}

  • C

    7.527×10237.527 \times 10^{23} and 0.125mol0.125 \, \text{mol}

  • D

    7.527×10227.527 \times 10^{22} and 0.250mol0.250 \, \text{mol}

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: Volume of O2O_2 is 2.8375L2.8375 \, \text{L} at STP.

Find: Number of molecules and moles.

At STP, one mole of a gas occupies

22.4L22.4 \, \text{L}

So, the number of moles of O2O_2 is

nO2=2.837522.4=0.125moln_{O_2} = \frac{2.8375}{22.4} = 0.125 \, \text{mol}

Now use Avogadro's number:

NA=6.022×1023mol1N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}

Therefore, number of molecules is

Molecules of O2=0.125×6.022×1023=7.527×1022\text{Molecules of } O_2 = 0.125 \times 6.022 \times 10^{23} = 7.527 \times 10^{22}

Therefore, the number of molecules and moles are 7.527×10227.527 \times 10^{22} and 0.125mol0.125 \, \text{mol} respectively. The correct option is A.

Alternative Working Noted in the solution

Given: Volume of O2O_2 is 2.8375L2.8375 \, \text{L} at STP.

Find: Number of moles and number of molecules.

A handwritten calculation showing number of moles from 2.8375 divided by 22.4 and molecules using Avogadro number multiplication.

One part of the solution mentions 22.7L22.7 \, \text{L} at STP, while another part uses 22.4L22.4 \, \text{L}. The final numerical answer shown matches the 22.4L22.4 \, \text{L} calculation used in the image and in Approach Solution 2.

Using

nO2=2.837522.4=0.125moln_{O_2} = \frac{2.8375}{22.4} = 0.125 \, \text{mol}

and then

Number of molecules=0.125×6.022×1023=7.527×1022\text{Number of molecules} = 0.125 \times 6.022 \times 10^{23} = 7.527 \times 10^{22}

we obtain the listed answer.

Hence, the defensible final answer from the solution is Option A.

Common mistakes

  • Using the wrong molar volume at STP without checking consistency. The solution contains both 22.7L22.7 \, \text{L} and 22.4L22.4 \, \text{L}, but the final answer matches 22.4L mol122.4 \, \text{L mol}^{-1}. Always verify which value the final calculation actually uses.

  • Interchanging molecules and moles in the final ordered pair. The question asks for molecules first and moles second, so the answer must be reported in that same order.

  • Forgetting to multiply the number of moles by Avogadro's number to get molecules. Moles and molecules are not the same quantity; use N=nNAN = nN_A after finding nn.

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