SME
General Chemistry II · Problem type
Molarity to molality and mass percent
Use this for “A 2.00 M NaCl solution has a density of 1.08 g/mL. Find its molality and mass percent.”
Diagram
Molarity is moles per liter: 2 mol in 1 L is 2 mol/L.
Each dot is 0.05 mol of solute: 40 dots.
This is an example. Type your own values to start a new problem.
c
Molarity
example · M
ρ
Solution density
example
M
Molar mass
example · g/mol
mₛ
Solute mass in 1 L
calculated · g
mₛₒₗₙ
Solution mass in 1 L
calculated · g
mₛₒₗᵥ
Solvent mass in 1 L
calculated · kg
b
Molality
calculated · mol/kg
w
Mass percent
calculated · %
Formulas
mₛ
=
c
×
M
116.9 = 2 × 58.44
mₛₒₗₙ
=
1,000
×
ρ
1,080 = 1,000 × 1.08
mₛₒₗᵥ
=
mₛₒₗₙ − mₛ
1,000
0.9631
=
1,080 − 116.9
1,000
b
=
c
mₛₒₗᵥ
2.077
=
2
0.9631
w
=
100
×
mₛ
mₛₒₗₙ
10.82
=
100
×
116.9
1,080
Assumptions
•
Work on 1 L (1000 mL) of solution: it holds c moles of solute, and its mass is 1000 × ρ grams.
•
The density is the solution’s, not water’s; the solvent is what is left once the solute’s mass is taken away.
•
Molality is moles of solute per kilogram of solvent; mass percent is the solute’s share of the solution’s mass.
Step-by-step
WE KNOW
c = 2 M, ρ = 1.08 g/mL, M = 58.44 g/mol
FIND
solute mass in 1 L (mₛ), solution mass in 1 L (mₛₒₗₙ), solvent mass in 1 L (mₛₒₗᵥ), molality (b), mass percent (w)
Step 1 · Find solute mass in 1 L (mₛ)
Use mₛ = c × M
One
liter
holds
c
moles;
times
the
molar
mass
gives
their
grams.
mₛ = 2 × 58.44
mₛ = 116.9 g
Step 2 · Find solution mass in 1 L (mₛₒₗₙ)
Use mₛₒₗₙ = 1,000 × ρ
A liter is 1000 mL; times the grams in each mL gives the solution’s mass.
mₛₒₗₙ = 1,000 × 1.08
mₛₒₗₙ = 1,080 g
Step 3 · Find solvent mass in 1 L (mₛₒₗᵥ)
Use mₛₒₗᵥ = (mₛₒₗₙ − mₛ) ÷ 1,000
Take
the
solute’s
grams
from
the
solution’s,
then
1000
for
kilograms.
mₛₒₗᵥ
=
1,080 − 116.9
1,000
mₛₒₗᵥ
=
963.1
1,000
mₛₒₗᵥ = 0.9631 kg
Step 4 · Find molality (b)
Use b = c ÷ mₛₒₗᵥ
The
c
moles
in
the
liter,
per
kilogram
of
solvent.
b
=
2
0.9631
b
=
2.077
mol/kg
Step 5 · Find mass percent (w)
Use w = 100 × mₛ ÷ mₛₒₗₙ
The solute’s grams over the solution’s, as a percent.
w
=
100
×
116.9
1,080
w
=
11,690
1,080
w
=
10.82%
Check
Put the numbers back in. Both sides should match.
116.9 = 2 × 58.44 ✓
1,080 = 1,000 × 1.08 ✓
0.9631
=
1,080 − 116.9
1,000
✓
2.077
=
2
0.9631
✓
10.82
=
100
×
116.9
1,080
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.