What volume (in mL) of water should be added to 50 ml of HNO 3 solution having density 1.5 g ml − 1 and 63.0% by weight to have one molar solution.

Question

What volume (in mL) of water should be added to 50 ml of HNO 3 ​ solution having density 1.5 g ml − 1 and 63.0% by weight to have one molar solution.

TestHub · Accepted Answer

To determine the volume of water needed, first calculate the moles of HNO₃ in the initial solution.

Volume of HNO₃ solution = $50 m L$

Density = $1.5 g / m L$

Mass of solution = $50 m L \times 1.5 g / m L = 75 g$

Mass of HNO₃ = $75 g \times 0.63 = 47.25 g$

Molar mass of HNO₃ = $1 + 14 + (3 \times 16) = 63 g / m o l$

Moles of HNO₃ = $\frac{47.25 g}{63 g / m o l} = 0.75 m o l$

For a $1 M$ solution, $1 m o l$ of solute is in $1 L$ of solution.

To have a $1 M$ solution with $0.75 m o l$ of HNO₃, the total volume must be $0.75 L$ , or $750 m L$ .

Volume of water to add = Total volume - Initial volume = $750 m L - 50 m L = 700 m L$ .

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