Concentrated hydrochloric acid is usually available at a concentration of 37.7 percent by mass. The density of the solution is 1.19gml−1 . What is its molar concentration?
The Correct Answer and Explanation is:
To calculate the molar concentration of concentrated hydrochloric acid (HCl) with a 37.7% mass concentration and a density of 1.19 g/mL, follow these steps:
Step 1: Understand the Information Given
- Mass concentration = 37.7% (which means 37.7 g of HCl per 100 g of solution).
- Density of solution = 1.19 g/mL (this tells us the mass of the solution per unit volume).
We need to determine the molar concentration of the solution, which is expressed in moles of HCl per liter of solution.
Step 2: Calculate the Mass of 1 Liter of Solution
The density formula is:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Rearranging the formula to find mass:
[
\text{Mass of 1 liter of solution} = \text{Density} \times \text{Volume}
]
[
\text{Mass of 1 liter of solution} = 1.19 \, \text{g/mL} \times 1000 \, \text{mL} = 1190 \, \text{g}
]
Step 3: Calculate the Mass of HCl in 1 Liter of Solution
Since the solution is 37.7% HCl by mass, we can find the mass of HCl in 1190 g of solution:
[
\text{Mass of HCl} = \frac{37.7}{100} \times 1190 \, \text{g} = 448.3 \, \text{g}
]
Step 4: Calculate the Moles of HCl
The molar mass of HCl is 36.46 g/mol. Now, we can calculate the number of moles of HCl:
[
\text{Moles of HCl} = \frac{\text{Mass of HCl}}{\text{Molar mass of HCl}} = \frac{448.3 \, \text{g}}{36.46 \, \text{g/mol}} = 12.3 \, \text{mol}
]
Step 5: Calculate the Molar Concentration
The molar concentration is the number of moles of HCl per liter of solution. Since we have 12.3 moles of HCl in 1 liter of solution, the molar concentration is:
[
\text{Molar concentration} = 12.3 \, \text{mol/L}
]
Final Answer:
The molar concentration of the hydrochloric acid solution is 12.3 M.
Explanation:
To determine the molar concentration of hydrochloric acid, we utilized the mass concentration and density of the solution. By calculating the mass of the solution in 1 liter, we could find how much HCl it contains. Then, dividing the mass of HCl by its molar mass allowed us to calculate the number of moles. Finally, the molar concentration was determined by dividing the moles of HCl by the volume of the solution in liters, resulting in a molarity of 12.3 M.