Multiple choice

A volume of $25 ml$ of $ (N/10)-Na_{2}CO_{3}$ solution neutralizes 10 ml of a dilute $ H_{2}SO_{4}$ solution. The volume of water that must be added to $400 ml$ of this $ H_{2}SO_{4}$ solution in order to make it exactly $N/10$ is

  1. $1000 ml$
  2. $600 ml$
  3. $500 ml$
  4. $400 ml$
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B Correct answer
Explanation

25 ml of N/10 Na2CO3 neutralizes 10 ml of H2SO4. The H2SO4 normality is (25 * 0.1) / 10 = 0.25 N. To dilute 400 ml of 0.25 N to 0.1 N, use N1V1 = N2V2: 0.25 * 400 = 0.1 * V2, so V2 = 1000 ml. Water to add = 1000 - 400 = 600 ml.

AI explanation

Using the normality equation N1V1 equals N2V2, the normality of the given sulfuric acid is found by multiplying the normality of sodium carbonate by its volume and dividing by the volume of the acid. The normality of the acid is (1/10 multiplied by 25) divided by 10, which equals 0.25 N. Let the volume of water to be added be V, so the final total volume is 400 plus V, and the final normality is 1/10. Setting up the equation 0.25 multiplied by 400 equals 1/10 multiplied by (400 plus V) gives 100 equals 40 plus 0.1V, meaning V equals 600 ml.

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