An aqueous solution of concentrated hydrobromic acid contains 48% HBr by mass. If the density of the solution is 1.5 g / mL, What is its concentration?

Question

Wyatt Adkins · Accepted Answer

(B): #8.9# #"mol/L"#

We're asked to find the (molar) concentration of #"HBr"# in solution, given its mass percentage and density.

To do this, we'll first assume there is #1# #"L"# of solution, so the density is also written as

#1.5# #"g/mL"# #= 1500# #"g/L"#

We're given that #48%# of the mass (#1500# #"g"#) is #"HBr"#, so the mass of #"HBr"# is

#0.48·1500# #"g soln"# #= ul(720color(white)(l)"g HBr"#

Now, we use the molar mass of #"HBr"# (#80.912# #"g/mol"#) to calculate the number of moles:

#720cancel("g HBr")((1color(white)(l)"mol HBr")/(80.912cancel("g HBr"))) = color(red)(8.9# #color(red)("mol HBr"#

Molarity equation:

#"molarity" = "mol solute"/"L soln"#

#= (color(red)(8.9color(white)(l)"mol HBr"))/(underbrace(1color(white)(l)"L soln")_"we assumed 1 L") = color(blue)(8.9color(white)(l)"mol/L"#

Thus, option (B) is the correct answer.

Wyatt Adkins · Answer

undefined The concentration of the solution in terms of molarity (M) can be calculated by using the mass percentage of HBr, the density of the solution, and the molar mass of HBr. The molar mass of HBr (hydrogen bromide) is approximately 1 (for H) + 79.9 (for Br) = 80.9 g/mol.

Given:

- Mass % of HBr = 48%
- Density of the solution = 1.5 g/mL

First, find the mass of HBr in 1000 mL (1 L) of solution, since molarity is moles of solute per liter of solution:

- Density = 1.5 g/mL, so the mass of 1000 mL of solution is 1.5 g/mL * 1000 mL = 1500 g.

- Since the solution is 48% HBr by mass, the mass of HBr in this mass of solution is 0.48 * 1500 g = 720 g.

Now, convert the mass of HBr to moles:

- Moles of HBr = mass of HBr / molar mass of HBr = 720 g / 80.9 g/mol = 8.9 mol (approximately).

Since these moles of HBr are in 1 L of solution, the molarity (M) of the solution is 8.9 M.