Question

$\text{HN}{{\text{O}}_{3}}$ used as a reagent has specific gravity of 1.42 g/mL and contains 70% by strength $\text{HN}{{\text{O}}_{3}}$.
Calculate the value of 100x if x mL is the volume of acid that contains 63 g pure acid:
A. 63.38
B. 63.00
C. 63.20
D. None of these

Answer 1

Hint: This question is based on density and percentage by strength of $\text{HN}{{\text{O}}_{3}}$. Use a unitary method to find the volume of acid. 1.42 g/mL means 1 mL of volume has 1.42 grams of $\text{HN}{{\text{O}}_{3}}$. 70% by strength means 70 grams of $\text{HN}{{\text{O}}_{3}}$ in 100 mL of volume.

Complete answer:
Let us start solving this question step by step:
Step (1) The density of $\text{HN}{{\text{O}}_{3}}$ solution is 1.42 g/mL means that 1 mL of volume has 1.42 grams of $\text{HN}{{\text{O}}_{3}}$ and 100 mL of volume has 70 grams of $\text{HN}{{\text{O}}_{3}}$.
So, the mass of pure $\text{HN}{{\text{O}}_{3}}$ in 100 mL of volume is $70\times 1.42$ grams or 99.4 grams.
Step (2) The volume of acid will be found by unitary method as
99.4 grams of pure acid is present in 100 mL of volume,
Then, 63 grams of pure acid will be present in $\dfrac{100\times 63}{99.4}$ mL of volume which is equal to 63.38 ml.
The volume of acid will be 63.38 mL of acid.
The value of 100x is 63.38 mL. As, we were already dealing with 100 mL of volume.
So, the correct answer is “Option A”.

Note: The specific gravity and density of any substance is not the same. Specific gravity is actually the relative density of any substance. The specific gravity is the density of any substance divided by the density of water. So, do not consider it the same. Here, we have taken it as density taking the density of water to be 1g/mL.