commercially available concentrated Hydrochloric acid is 37.0% w/w Hcl.its density is 1.18g/ml.using this information calculate (a)the molarity of concentrated Hcl,and (b)the mass and volume (in ml)of solution containing 0.315 mol of Hcl?
grams HCl in 1000 mL is
1.18 g/mL x 1000 mL x 0.37 = approx 437 g but that's just an estimate.
Then mols in that 1 L = grams/molar mass = approx 437/36.5 = about 12 M, another estimate.
Since that is mols/L that is M.
b.
g HCl = mols HCl x molar mass HCl so g HCl = 0.315 x 36.5 = approx 11.5 g. Substitute the 11.5 g HCl into the formula below (the same I used above for grams HCl--but then in 1000 mL) and solve for mL. I get about 26 mL.
density x vol x % = grams
Mass
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To calculate the molarity of concentrated HCl, first, we need to determine the molar mass of HCl.
Molar mass of HCl = Atomic mass of H + Atomic mass of Cl
= (1.008 g/mol) + (35.453 g/mol)
= 36.461 g/mol
(a) Molarity of concentrated HCl:
Molarity (M) is defined as the number of moles of solute per liter of solution.
Molarity (M) = (mass of solute in grams) / (molar mass of solute in g/mol) / (volume of solution in L)
Given that the concentration of HCl is 37.0% w/w, it means 37.0 g of HCl is present in 100 g of solution.
The mass of HCl in the solution = 37.0 g
Volume of the solution can be determined using the density of the solution:
Density = (mass of substance) / (volume of substance)
Rearranging the equation to solve for volume:
Volume of the solution = (mass of the substance) / (density of the substance)
Given that the density of HCl solution is 1.18 g/mL, we can substitute the values:
Volume of the solution = 37.0 g / 1.18 g/mL
Volume of the solution = 31.36 mL
Converting the volume from milliliters to liters:
Volume of the solution = 31.36 mL * (1 L / 1000 mL)
Volume of the solution = 0.03136 L
Now, we can calculate the molarity:
Molarity = (mass of solute in grams) / (molar mass of solute in g/mol) / (volume of solution in L)
Molarity = 37.0 g / 36.461 g/mol / 0.03136 L
Calculating the molarity gives us:
Molarity = 37.0 g / (36.461 g/mol) / 0.03136 L
Molarity ≈ 10.07 M
Therefore, the molarity of the concentrated HCl is approximately 10.07 M.
(b) To calculate the mass and volume of the solution containing 0.315 mol of HCl, we can use the molarity equation:
Molarity = (moles of solute) / (volume of solution in L)
Rearranging the equation to solve for volume:
Volume of solution = (moles of solute) / (molarity)
Given that we have 0.315 mol of HCl, we can substitute the values:
Volume of solution = 0.315 mol / 10.07 M
Volume of solution ≈ 0.03125 L
Converting the volume from liters to milliliters:
Volume of solution = 0.03125 L * (1000 mL / 1 L)
Volume of solution ≈ 31.25 mL
To calculate the mass of the solution, we need to use the concentration of the solution.
The mass percent of HCl in the solution is 37.0% w/w, meaning 37.0 g of HCl is present in 100 g of the solution.
Let's assume we have x grams of the solution.
Mass of HCl in the solution = (37.0 g HCl / 100 g solution) * x
Since the concentration is given to be 37.0% w/w, the percentage of solution is (100% - 37.0%) = 63.0%.
Mass of the solution = (63.0 g / 100 g solution) * x
We know that the mass of the solution is equal to the sum of the masses of HCl and the remaining solution:
Mass of HCl in the solution + Mass of the solution = x
Substituting the values:
(37.0 g HCl / 100 g solution) * x + (63.0 g / 100 g solution) * x = x
Simplifying the equation:
(37 x + 63 x) / 100 g solution = x
Solving for x:
100 x = 100 g solution
Therefore, the mass of the solution is 100 g.
Thus, the mass and volume of the solution containing 0.315 mol of HCl are approximately 100 g and 31.25 mL, respectively.