A 38.5 mL sample of HBr is titrated with 112 mL of 1.05 mol/L KOH. The density of the HBr solution is 1.75 g/mL. Calculate the percentage by mass of the HBr in the sample.
How come we don't use density*volume to find the moles of HBr?
Because mols is not equal to d*v.
mass (grams) HBr soluton = density x volume = approx 67 g as the mass of that 38.5 mL sample.
How much HBr is in that 38.5 mL sample?
That's mols KOH = M x L = ?
Using the coefficients in the balanced equation, convert mols KOH to mols HBr.
Then mols HBr = grams HBr/molar mass HBr. You know molar mass and mols, solve for grams HBr in the 38.5 mL.
Then %HBr by mass = (mass HBr/mass sample)*100 = ?
mols HBr = grams HBr/molar mass HBr.
The reason we do not use density times volume to find the moles of HBr in this case is because we can directly determine the moles of HBr through the reaction stoichiometry. The balanced chemical equation for the reaction between HBr and KOH is:
HBr + KOH → KBr + H2O
From this equation, we can determine the mole ratio between HBr and KOH as 1:1. This means that for every mole of HBr, we require exactly one mole of KOH to react completely.
In the given problem, we are provided with the volume and concentration of KOH used in the titration. As the concentration of KOH is given, we can easily determine the number of moles of KOH used in the reaction by multiplying the volume by the concentration:
moles of KOH = volume (L) × concentration (mol/L) = 0.112 L × 1.05 mol/L = 0.1176 mol KOH
Since the mole ratio between HBr and KOH is 1:1, this means that the number of moles of HBr in the sample is also 0.1176 mol.
To calculate the percentage by mass of HBr in the sample, we need to determine the mass of HBr and divide it by the mass of the entire sample. The mass of HBr can be calculated using its molar mass, which is approximately 80.91 g/mol.
mass of HBr = moles of HBr × molar mass of HBr = 0.1176 mol × 80.91 g/mol = 9.51 g
Now, to calculate the mass of the entire sample, we multiply the density of the HBr solution (1.75 g/mL) by the volume of the sample (38.5 mL):
mass of sample = density × volume = 1.75 g/mL × 38.5 mL = 67.38 g
Finally, we can calculate the percentage by mass of HBr in the sample:
percentage by mass of HBr = (mass of HBr / mass of sample) × 100% = (9.51 g / 67.38 g) × 100% = 14.11%
To find the moles of HBr in the sample, we use the molarity of the KOH solution and the volume of KOH used in the titration. The balanced chemical equation for the reaction between HBr and KOH is:
HBr + KOH → KBr + H2O
From the equation, we can see that the molar ratio between HBr and KOH is 1:1. This means that for every 1 mole of HBr, we will react with 1 mole of KOH.
In this titration, we have been given the volume of KOH used (112 mL) and its molarity (1.05 mol/L). Using the formula:
moles = volume × concentration
we can calculate the moles of KOH used in the titration:
moles KOH = 112 mL × 1.05 mol/L = 117.6 mmol
Since the molar ratio between HBr and KOH is 1:1, the moles of HBr present in the sample will also be 117.6 mmol.
Now, to find the mass of HBr in the sample, we need to convert the moles of HBr to grams. To do this, we need the molar mass of HBr, which can be calculated by adding the atomic masses of hydrogen (1.01 g/mol) and bromine (79.90 g/mol).
molar mass HBr = 1.01 g/mol (H) + 79.90 g/mol (Br) = 80.91 g/mol
Now we can calculate the mass of HBr in the sample:
mass HBr = moles HBr × molar mass HBr = 117.6 mmol × 80.91 g/mol = 9.52 g
Finally, to calculate the percentage by mass of HBr in the sample, we need to divide the mass of HBr by the total mass of the sample (given by the density of the HBr solution):
total mass of sample = density × volume = 1.75 g/mL × 38.5 mL = 66.98 g
percentage by mass = (mass HBr / total mass of sample) × 100 = (9.52 g / 66.98 g) × 100 ≈ 14.20%
So the percentage by mass of HBr in the sample is approximately 14.20%.
In this specific calculation, we don't use the density of the HBr solution because we are not directly interested in the volume of the HBr sample. We can find the moles of HBr directly from the volume and concentration of KOH used in the titration, and then calculate the mass of HBr using the molar mass. The density of the HBr solution is only used to calculate the total mass of the sample for the final percentage calculation.