Concentrated HCl has a specific gravity of 1.18 and contains 37% by weight HCl. Specific gravity is interpreted as density in grams per milliliter. Calculate the molarity of concentrated HCl, and determine how much concentrated acid should be diluted to 1 L to make 0.1 M HCl.
The Correct Answer and Explanation is:
To calculate the molarity of concentrated HCl, we need to break down the information and apply a few key steps:
Step 1: Determine the density of concentrated HCl.
The specific gravity of concentrated HCl is given as 1.18, which means the density is 1.18 g/mL.
Step 2: Find the mass of HCl in 1 liter of concentrated acid.
We know the density is 1.18 g/mL, so the mass of 1 liter (1000 mL) of concentrated HCl is:Mass of solution=Density×Volume\text{Mass of solution} = \text{Density} \times \text{Volume}Mass of solution=Density×VolumeMass of solution=1.18 g/mL×1000 mL=1180 g\text{Mass of solution} = 1.18 \, \text{g/mL} \times 1000 \, \text{mL} = 1180 \, \text{g}Mass of solution=1.18g/mL×1000mL=1180g
Next, since the solution is 37% by weight HCl, the mass of HCl in 1180 grams of solution is:Mass of HCl=37%×1180 g=0.37×1180 g=436.6 g\text{Mass of HCl} = 37\% \times 1180 \, \text{g} = 0.37 \times 1180 \, \text{g} = 436.6 \, \text{g}Mass of HCl=37%×1180g=0.37×1180g=436.6g
Step 3: Convert the mass of HCl to moles.
The molar mass of HCl is approximately 36.46 g/mol. To find the moles of HCl in the solution:Moles of HCl=Mass of HClMolar mass of HCl\text{Moles of HCl} = \frac{\text{Mass of HCl}}{\text{Molar mass of HCl}}Moles of HCl=Molar mass of HClMass of HClMoles of HCl=436.6 g36.46 g/mol≈11.97 mol\text{Moles of HCl} = \frac{436.6 \, \text{g}}{36.46 \, \text{g/mol}} \approx 11.97 \, \text{mol}Moles of HCl=36.46g/mol436.6g≈11.97mol
Step 4: Calculate the molarity of the concentrated HCl.
Molarity (M) is defined as the number of moles of solute per liter of solution. Since we have 1 liter of solution:Molarity of concentrated HCl=11.97 mol1 L≈12.0 M\text{Molarity of concentrated HCl} = \frac{11.97 \, \text{mol}}{1 \, \text{L}} \approx 12.0 \, \text{M}Molarity of concentrated HCl=1L11.97mol≈12.0M
Thus, the molarity of the concentrated HCl is approximately 12.0 M.
Step 5: Determine the volume of concentrated acid needed to make 0.1 M HCl.
To dilute the concentrated HCl to a 0.1 M solution, we use the dilution equation:M1V1=M2V2M_1V_1 = M_2V_2M1V1=M2V2
Where:
- M1=12.0 MM_1 = 12.0 \, \text{M}M1=12.0M (initial molarity),
- V1V_1V1 is the volume of concentrated acid required,
- M2=0.1 MM_2 = 0.1 \, \text{M}M2=0.1M (final molarity),
- V2=1 LV_2 = 1 \, \text{L}V2=1L (final volume).
Now, solve for V1V_1V1:12.0 M×V1=0.1 M×1 L12.0 \, \text{M} \times V_1 = 0.1 \, \text{M} \times 1 \, \text{L}12.0M×V1=0.1M×1LV1=0.1 M×1 L12.0 M=0.112 L=0.00833 LV_1 = \frac{0.1 \, \text{M} \times 1 \, \text{L}}{12.0 \, \text{M}} = \frac{0.1}{12} \, \text{L} = 0.00833 \, \text{L}V1=12.0M0.1M×1L=120.1L=0.00833LV1≈8.33 mLV_1 \approx 8.33 \, \text{mL}V1≈8.33mL
Final Answer:
- The molarity of concentrated HCl is 12.0 M.
- To make 1 liter of 0.1 M HCl, you will need to dilute 8.33 mL of the concentrated HCl solution.
