Question

Sulfuric acid is used in the synthesis and processing of many chemicals and metals, and it is the electrolyte in common lead-acid batteries.
It is used in various strengths, ranging from concentrated (100%) to dilute; so being able to estimate its concentration from a simple measurement of specific gravity is quite useful.
Suppose you prepare a solution that is 20 wt% H₂SO₄ in water and intend to confirm the concentration by comparing the specific gravity of the solution to that available from the literature.
To 80 g of water you carefully add 20 g of H₂SO₄ and allow the resulting mixture to equilibrate at 20°C.
(You know that rapidly adding the acid to water or water to concentrated acid can both lead to dangerous splatters of liquid.)

1. From the component specific gravities, estimate the volumes of water and sulfuric acid that have been blended in mL. V_water=   mL V_{sulfuric acid}= mL

2. What is the density of the 20 wt% sulfuric acid assuming that the volumes are additive in g/mL?

3. Perry's Chemical Engineer's Handbook lists the specific gravity of sulfuric acid as a function of both acid concentration and temperature.
The value for 20 wt% sulfuric acid at 20°C is listed as 1.1394.
What is the volume of the 20 wt% sulfuric acid solution prepared as described by the above process in mL?

4. What is the volume of 40 wt% sulfuric acid (SG = 1.2991 at 25°C) that must be added to the 100.0 g of the 20-wt% solution to produce a solution that is 35 wt% sulfuric acid in mL?

Answer 1

(1) Specific gravity of $H_2SO_4 =1.834$
From the formula Specific gravity $= \frac {\delta _{H_2SO_4}}{\delta _{Water} }$

Therefore density of H2SO4$= {\delta _{H_2SO_4}}= 1.834 \times {\delta _{Water} }$= 1.834 g/ml

In $20\%$ by solution of $H_2SO_4$ we mixed = $20g \ H_2SO_4 + 80 g \ Water$

$V_{Water} = \frac{80g}{\delta _{water}} =\frac{80g}{1 g/ml}= 80 ml$

$V_{H_2SO_4} = \frac{20g}{\delta _{H_2SO_4}} =\frac{20g}{1.834 g/ml}= 10.90 ml$

Total volume = $V_{H_2SO_4}+ V_{water}= 80+ 10.90 = 90.90 ml$

(2) the density of the 20 wt% sulfuric acid assuming that the volumes are additive in g/mL

Density of $20wt\% = [(\frac{10.90 ml}{90.90ml})\times 1.834] + [(\frac{80 ml}{90.90ml})\times 1]$

$\Rightarrow = 0.220 + 0.880= 1.10 g/ml$

(3) Specific gravity of 20wt % solution of H2SO4= 1.1394 g/ml

volume $= \frac{(80 g H_2O + 20 g H_2SO_4)}{1.1394g/ml} = 87.76ml$

(4) the volume of 40 wt% sulfuric acid (SG = 1.2991 at 25°C) that must be added to the 100.0 g of the 20-wt% solution to produce a solution that is 35 wt% sulfuric acid in ml

If the amount used to prepare 40 wt% H2SO4 is $w$

$\Rightarrow w$ = amount of 40 wt%

Total weight

$\Rightarrow 0.40w + 0.20(100g) = 0.35(100 + w)$

$\Rightarrow 0.40w - 0.35w = 35-20$

$\Rightarrow 0.05w = 15$

$\Rightarrow w = \frac{15}{0.05}= 300 g$

$300g = \frac{300g}{1.2991g/ml}= 230.93 ml$