To find the molarity (M) of a solution given its molality (m = 0.0480 mol/kg for LiF) and density (1.10 g/mL), you can use the relationship between molality and molarity:
m=Mρ−M×MWm=\frac{M}{\rho -M\times MW}m=ρ−M×MWM
where:
- mmm = molality (mol/kg solvent) = 0.0480
- MMM = molarity (mol/L solution) - unknown
- ρ\rho ρ = density of solution (g/mL) = 1.10
- MWMWMW = molar mass of solute (LiF) = 25.94 g/mol
Rearranging the formula to solve for molarity MMM:
M=m×ρ1+m×MWM=\frac{m\times \rho}{1+m\times MW}M=1+m×MWm×ρ
Alternatively, the formula can be expressed as:
m=1000M1000ρ−M×MWm=\frac{1000M}{1000\rho -M\times MW}m=1000ρ−M×MW1000M
Using the data:
- Convert density to g/L: 1.10 g/mL=1100 g/L1.10,g/mL=1100,g/L1.10g/mL=1100g/L
- Plug values into the rearranged formula:
0.0480=1000M1000×1.10−M×25.940.0480=\frac{1000M}{1000\times 1.10-M\times 25.94}0.0480=1000×1.10−M×25.941000M
0.0480(1100−25.94M)=1000M0.0480(1100-25.94M)=1000M0.0480(1100−25.94M)=1000M
52.8−1.245M=1000M52.8-1.245M=1000M52.8−1.245M=1000M
52.8=1001.245M52.8=1001.245M52.8=1001.245M
M=52.81001.245≈0.0527 mol/LM=\frac{52.8}{1001.245}\approx 0.0527,\text{mol/L}M=1001.24552.8≈0.0527mol/L
So, the molarity of the solution is approximately 0.0528 M
. This matches the typical calculation for converting molality to molarity when density and molar mass are known.
