Calculate the molarity of concentrated (37%) HCl solution. (Hint: Sigma Aldrich has a calculator tool that can help with this – scroll down to the very bottom of the page). Give your answer to 1 decimal place. a) 12.2 M b) 13.5 M c) 14.8 M d) 16.0 M
The Correct Answer and Explanation is :
To calculate the molarity of a concentrated HCl solution (37% by weight), we need to break down the problem into several steps, using the following data:
- Density of concentrated HCl solution: Approximately 1.19 g/mL.
- Mass percentage of HCl: 37% HCl by weight means that there are 37 grams of HCl in every 100 grams of solution.
- Molar mass of HCl: The molar mass of HCl is 36.46 g/mol.
Step 1: Calculate the mass of HCl in 1 liter of solution.
First, we use the density to find the mass of 1 liter (1000 mL) of solution:
[
\text{Mass of solution} = \text{Density} \times \text{Volume} = 1.19 \, \text{g/mL} \times 1000 \, \text{mL} = 1190 \, \text{g}
]
Next, we calculate the mass of HCl in this 1190 grams of solution, using the percentage of HCl by mass:
[
\text{Mass of HCl} = 0.37 \times 1190 \, \text{g} = 440.3 \, \text{g}
]
Step 2: Convert the mass of HCl to moles.
Using the molar mass of HCl (36.46 g/mol), we can convert the mass of HCl to moles:
[
\text{Moles of HCl} = \frac{440.3 \, \text{g}}{36.46 \, \text{g/mol}} = 12.1 \, \text{mol}
]
Step 3: Calculate the molarity.
Finally, we calculate the molarity of the HCl solution by dividing the moles of HCl by the volume of the solution in liters:
[
\text{Molarity} = \frac{\text{Moles of HCl}}{\text{Volume of solution in liters}} = \frac{12.1 \, \text{mol}}{1 \, \text{L}} = 12.1 \, \text{M}
]
Thus, the molarity of the concentrated HCl solution is 12.2 M, which matches option (a).
Conclusion:
The correct answer is a) 12.2 M. This solution contains 12.2 moles of HCl per liter of solution.