Given density of the solution is 1.44 g/cm^3.
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's how to determine the concentration of the stock solution:
Step 1: Calculate the mass of 1 litre of the solution.
Given density of the solution is $1.44 \, \text{g/cm}^3$.
Since $1 \, \text{L} = 1000 \, \text{cm}^3$:
$$ \text{Mass of 1 L of solution} = \text{Density} \times \text{Volume} $$
$$ \text{Mass of 1 L of solution} = 1.44 \, \text{g/cm}^3 \times 1000 \, \text{cm}^3 = 1440 \, \text{g} $$
Step 2: Calculate the mass of pure nitric acid (HNO$_3$) in 1 litre of the solution.
The percentage purity is $65\%$.
$$ \text{Mass of pure HNO}_3 = \text{Mass of solution} \times \text{Purity percentage} $$
$$ \text{Mass of pure HNO}_3 = 1440 \, \text{g} \times 0.65 = 936 \, \text{g} $$
Step 3: Calculate the number of moles of pure nitric acid in 1 litre of the solution.
The formula mass of HNO$_3$ is $63 \, \text{g/mole}$.
$$ \text{Moles of HNO}_3 = \frac{\text{Mass of pure HNO}_3}{\text{Formula mass}} $$
$$ \text{Moles of HNO}_3 = \frac{936 \, \text{g}}{63 \, \text{g/mole}} \approx 14.857 \, \text{moles} $$
Step 4: Determine the concentration in moles per litre.
Concentration (Molarity) is the number of moles per litre of solution.
$$ \text{Concentration} = \frac{\text{Moles of HNO}_3}{\text{Volume of solution (L)}} $$
$$ \text{Concentration} = \frac{14.857 \, \text{moles}}{1 \, \text{L}} \approx 14.86 \, \text{mol/L} $$
The concentration of the stock solution is approximately $\boxed{\text{14.86 mol/L}}$.
