Question

what volume of 98% $H_2SO_4$ by weight (d=1.85 g/ml) and what mass of water must be taken to prepare 100 ml of 15% $H_2SO_4$ solution (d= 1.1 g/ml) ?

Answer 1

Volume of 98% $H_2SO_4$ = 9.1 ml, Mass of water = 93 g

Answer 2

1. Calculate the mass of the final solution: Mass of final solution = Volume $\times$ Density = 100 ml $\times$ 1.1 g/ml = 110 g.

2. Calculate the mass of pure $H_2SO_4$ required in the final solution: Mass of pure $H_2SO_4$ = 15% of 110 g = 0.15 $\times$ 110 g = 16.5 g.

3. Calculate the mass of the concentrated 98% $H_2SO_4$ solution needed: Let $m_{\text{conc}}$ be the mass of the concentrated solution. 0.98 $\times m_{\text{conc}}$ = 16.5 g $m_{\text{conc}}$ = 16.5 g / 0.98 $\approx$ 16.84 g.

4. Calculate the volume of the concentrated 98% $H_2SO_4$ solution: Volume of concentrated solution = $m_{\text{conc}}$ / Density = 16.84 g / 1.85 g/ml $\approx$ 9.10 ml.

5. Calculate the mass of water to be added: Mass of water = Mass of final solution - Mass of concentrated $H_2SO_4$ solution Mass of water = 110 g - 16.84 g $\approx$ 93.16 g.

Rounding to appropriate significant figures (2 significant figures based on 15% and 1.1 g/ml), we get: Volume of 98% $H_2SO_4$ $\approx$ 9.1 ml Mass of water $\approx$ 93 g.