Multiple choice

Find out the volume of $98\%$ (w/w) $\displaystyle H_{2}SO_{4}$ (density $= 1.8$ g/ml) that must be diluted to prepare $12.0$ litres of $2.4\; M$ sulphuric acid solution.

  1. $1.6$ L
  2. $1.8$ L
  3. $2.3$ L
  4. $2.8$ L
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A Correct answer
Explanation

Molarity of 98% H2SO4 = (1000 * 1.8 * 0.98) / 98 = 18 M. Using M1V1 = M2V2: 18 * V1 = 2.4 * 12. V1 = (2.4 * 12) / 18 = 1.6 L.

AI explanation

Calculate the moles of sulphuric acid needed for the final solution by multiplying the target volume and molarity, which gives 12.0 liters multiplied by 2.4 moles per liter, resulting in 28.8 moles. Next, find the molarity of the concentrated acid by using the formula (mass percentage * density * 10) divided by molar mass, yielding (98 * 1.8 * 10) / 98 = 18 M. Finally, use the dilution formula M1V1 = M2V2, so 18 M multiplied by V1 equals 2.4 M multiplied by 12 liters, which gives the required volume as 1.6 liters.

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