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NVAEasyJEE 2025Concentration Terms (Molarity, Molality, etc.)

JEE Chemistry 2025 Question with Solution

20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is _____ x 10−210^{-2} M. (Nearest integer)

Answer

Correct answer:57

Step-by-step solution

Standard Method

Given: 20 mL of 2 M NaOH solution is mixed with 400 mL of 0.5 M NaOH solution.

Find: The integer in the form _____ x 10−210^{-2} M for the final concentration.

Use moles = molarity x volume in litres.

Moles in first solution=2×0.020=0.040 mol\text{Moles in first solution} = 2 \times 0.020 = 0.040 \text{ mol}Moles in second solution=0.5×0.400=0.200 mol\text{Moles in second solution} = 0.5 \times 0.400 = 0.200 \text{ mol}Total moles=0.040+0.200=0.240 mol\text{Total moles} = 0.040 + 0.200 = 0.240 \text{ mol}Total volume=20 mL+400 mL=420 mL=0.420 L\text{Total volume} = 20 \text{ mL} + 400 \text{ mL} = 420 \text{ mL} = 0.420 \text{ L}Final concentration=0.2400.420=0.571 M\text{Final concentration} = \frac{0.240}{0.420} = 0.571 \text{ M}

Now express it as x×10−2x \times 10^{-2} M:

0.571 M=57.1×10−2 M0.571 \text{ M} = 57.1 \times 10^{-2} \text{ M}

Nearest integer = 57.

Therefore, the required answer is 57.

Using additive moles and total volume

Given: Two NaOH solutions are mixed.

  • First: 20 mL, 2 M
  • Second: 400 mL, 0.5 M

Find: Final concentration written as _____ x 10−210^{-2} M.

First convert volumes into litres:

20 mL=0.020 L,400 mL=0.400 L20 \text{ mL} = 0.020 \text{ L}, \qquad 400 \text{ mL} = 0.400 \text{ L}

Calculate moles of solute in each solution:

0.020×2=0.040 mol0.020 \times 2 = 0.040 \text{ mol}0.400×0.5=0.200 mol0.400 \times 0.5 = 0.200 \text{ mol}

Add the moles:

0.040+0.200=0.240 mol0.040 + 0.200 = 0.240 \text{ mol}

Add the volumes:

0.020+0.400=0.420 L0.020 + 0.400 = 0.420 \text{ L}

Now compute the molarity of the mixture:

M=0.2400.420≈0.5714M = \frac{0.240}{0.420} \approx 0.5714

So,

0.5714 M=57.14×10−2 M0.5714 \text{ M} = 57.14 \times 10^{-2} \text{ M}

Rounding to the nearest integer gives 57.

The solution shows 6, but the worked calculation clearly gives 57. Hence the answer derived from the solution working is 57.

Common mistakes

  • Adding molarities directly is incorrect because concentration depends on both moles and total volume. First calculate moles of NaOH in each solution, then divide by the combined volume.

  • Using volumes in mL directly in moles=M×V\text{moles} = M \times V is wrong because molarity uses litres. Convert 20 mL to 0.020 L and 400 mL to 0.400 L before multiplying.

  • Forgetting to add the two volumes gives an incorrect final molarity. After mixing, the total volume is 420 mL or 0.420 L, not just the larger initial volume.

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