Calculate the volume of concentrated (98% v.v) H2SO4 that you will need to prepare 250ml of an 5.4 M H2SO4 solution.Density of 98% v.v H2SO4 = 1.84 g/cm3
I am having difficulty understanding the problem and units. The concentration of H2SO4 is 98% (v/v). Surely not. I suspect that is 98% w/w. That makes sense. 98% v/v means 98 mL pure H2SO4/100 mL H2SO4 solution. I've never seen 100% H2SO4 although it can be made by infusing 98% w/w H2SO4 with gaseous SO3 to make fuming H2SO4. Nor do I understand the statement that 98% v/v H2SO4 has a density of 1.84 g/cc. It's my understanding that 98% w/w H2SO4 has a density of 1.84 g/cc.
If you mean 98% w/w having a density of 1.84 g/cc then the problem is worked this way.
1.84 g/cc x 1000 cc x 0.98 x (1/98) = 18.4 M for that solution. Then if you wish to prepare 250 mL of a 5.4 M solution, use the dilution formula of
mL1 x M1 = mL2 x M2
mL1 x 18.4 = 250 mL x 5.4M. Solve for mL1, pipet that volume of the 98% stuff into a 250 mL volumetric flask holding about 125 or so mL distilled H2O, let cool, make to the mark with distilled water, stopper, mix thoroughly,, label. Done.
To calculate the volume of concentrated H2SO4 needed, we can use the equation:
(Volume of concentrated H2SO4) × (Concentration of H2SO4) × (Density of H2SO4) = (Volume of final solution) × (Concentration of final solution)
Let's plug in the given values:
Let the volume of concentrated H2SO4 be Vconcentrated.
Concentration of H2SO4 = 98% v.v = 98/100 = 0.98
Density of 98% v.v H2SO4 = 1.84 g/cm³
Volume of final solution = 250 ml
Concentration of final solution = 5.4 M
Now we can solve for Vconcentrated:
Vconcentrated × 0.98 × 1.84 g/cm³ = 250 ml × 5.4 M
Rearranging the equation to solve for Vconcentrated:
Vconcentrated = (250 ml × 5.4 M) / (0.98 × 1.84 g/cm³)
Calculating the value:
Vconcentrated = (1350) / (1.7992)
Vconcentrated ≈ 750 ml
Therefore, you will need approximately 750 ml of concentrated H2SO4 to prepare 250 ml of a 5.4 M H2SO4 solution.