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Step-by-Step Solution
Step 1: Understand What Is Being Asked
We need to find the volume of concentrated sulphuric acid (which is 98% by mass and has a density of 1.80 g/mL) required to prepare 1 L (1000 mL) of 0.1 M H2SO4 solution.
Step 2: Note Key Information About the Concentrated Acid
Concentration (by mass): 98% H2SO4.
Density of the acid: 1.80 g/mL.
From this, we can compute its normality by considering that H2SO4 is diprotic (provides 2 H+ ions per molecule).
Step 3: Calculate Normality of the Concentrated Acid
The equivalent weight of H2SO4 is 49 g/equivalent (since its molar mass is 98 g/mol and it provides 2 equivalents per mole). Using the density and mass percentage, for every 1 mL of solution:
Mass of the acid solution in 1 mL = $1.80\,\text{g}$
Mass of pure H2SO4 in that 1.80 g = 98% of 1.80 g = $1.80 \times 0.98 = 1.764\,\text{g}$
The normality ($N_1$) of the acid can be found by the formula:
$N_1 = \dfrac{\text{mass of H}_2\text{SO}_4 \text{ per mL}}{\text{equivalent weight of H}_2\text{SO}_4} \times 1000 \,$ (because 1 mL is involved, and we scale to 1 liter)
Often, this is simplified to the stated result:
$$
N_1 = \frac{98 \times 1.8 \times 10}{49} = 36\,\text{N}
$$
Step 4: Determine the Required Normality of the Final Solution
The desired solution is 0.1 M H2SO4. For sulphuric acid (diprotic), normality is twice its molarity (because each mole of H2SO4 can furnish 2 equivalents of H+):
Required normality ($N_2$) = $0.1 \,\text{M} \times 2 = 0.2 \,\text{N}$
Step 5: Use the Dilution Formula to Find the Volume of Concentrated Acid
According to the formula:
$$
N_1 V_1 = N_2 V_2
$$
where:
$N_1 = 36\,\text{N}$ (the normality of the concentrated acid)
$V_1$ = volume of the concentrated acid required (in mL)
$N_2 = 0.2\,\text{N}$ (the normality of the final solution)
$V_2 = 1000\,\text{mL}$ (total volume of the final solution)
Plug the known values in:
$36 \times V_1 = 0.2 \times 1000$
$V_1 = \dfrac{0.2 \times 1000}{36} = 5.55\,\text{mL}$
Step 6: State the Final Answer
The volume of the concentrated (98%) sulphuric acid of density 1.80 g/mL required to prepare 1 L of 0.1 M H2SO4 is 5.55 mL.
