The concentration (M) of HCl in a solution prepared by dissolving 5.5 g of HCl in 200 g of C2H6O
is ?????? M. The density of the solution is 0.79 g/mL.
A) 21 B) 0.93 C) 6.0 × 10-4 D) 1.72 E) 0.58
To find the concentration of HCl in the solution, we need to convert the mass of HCl and the volume of the solution into moles.
Step 1: Convert the mass of HCl to moles.
The molar mass of HCl is 36.46 g/mol.
Number of moles of HCl = mass of HCl / molar mass of HCl
Number of moles of HCl = 5.5 g / 36.46 g/mol
Number of moles of HCl ≈ 0.151 mol
Step 2: Convert the volume of the solution to liters.
Given that the density of the solution is 0.79 g/mL, we can calculate the volume of the solution.
Volume of the solution = mass of the solution / density of the solution
Volume of the solution = 200 g / 0.79 g/mL
Volume of the solution ≈ 253.16 mL
Since 1 L = 1000 mL, the volume of the solution in liters is 0.25316 L.
Step 3: Calculate the concentration of HCl in the solution.
Concentration (Molarity) = Number of moles of solute / Volume of solution (in liters)
Concentration of HCl = 0.151 mol / 0.25316 L
Concentration of HCl ≈ 0.596 M
Therefore, the concentration of HCl in the solution is approximately 0.596 M, which is closest to option E) 0.58.
To find the concentration (M) of HCl in the solution, we need to use the formula:
Molarity (M) = moles of solute / volume of solution in liters
First, we need to find the number of moles of HCl:
1. Convert the mass of HCl from grams to moles.
- The molar mass of HCl is 36.5 g/mol.
Moles of HCl = mass of HCl / molar mass of HCl
= 5.5 g / 36.5 g/mol
2. Convert the mass of the solution from grams to liters.
- The density of the solution is given as 0.79 g/mL, which means 0.79 g of the solution occupies 1 mL.
Volume of solution = mass of solution / density of solution
= 200 g / 0.79 g/mL
= 253.2 mL
Since we need the volume in liters, we divide by 1000:
Volume of solution = 253.2 mL / 1000 mL/L
= 0.2532 L
Now, substitute the values into the molarity formula:
Molarity (M) = moles of solute / volume of solution in liters
= (5.5 g / 36.5 g/mol) / 0.2532 L
Simplify the expression:
Molarity (M) = 0.152 moles / 0.2532 L
Finally, calculate the molarity:
Molarity (M) ≈ 0.6 M
Therefore, the concentration of HCl in the solution is approximately 0.6 M.
Looking at the given options, none of them match exactly. However, option C (6.0 × 10^(-4) M) is the closest.
M = mols/L
moles HCl = 5.5/molar mass HCl = ??
volume = mass of soln/density
mass of soln = 5.5 + 200 = 200.5 g.