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Chapter 13: Problem 20

The concentrated sulfuric acid we use in the laboratory is 98.0 percent \(\mathrm{H}_{2} \mathrm{SO}_{4}\) by mass. Calculate the molality and molarity of the acid solution. The density of the solution is \(1.83 \mathrm{~g} / \mathrm{mL}\).

Short Answer

Expert verified
In order to find the molality and molarity of the solution, one has to find the moles and mass of the solute, calculate the mass and volume of the solvent, and apply these values to the formula for molality and molarity.

Step by step solution

01

Calculation of the moles and mass of solute

Given that the H2SO4 solution is 98.0 percent by mass, the mass of H2SO4 in a 100g solution is 98g. This mean within one kg of the solution, the mass of H2SO4 is 980g. Now calculate the moles of H2SO4 using the molar mass (98.079 g/mol), \[ moles of H2SO4 = \frac {mass} {molar mass} = \frac {980 g} {98.079 g/mol} \]. Similarly, the mass of solvent (water, in this case, since we're talking about an aqueous solution) can also be found. If there are 980g of H2SO4 in 1kg solution, the remaining is water. So, the mass of water = 1kg - mass of H2SO4 in kg.
02

Calculation of the molality

With the moles of solute and mass of solvent from step 1, molality can now be calculated using the formula: \[ Molality (m) = \frac {moles of solute} {mass of solvent (in kg)} \].
03

Calculation of the volume of solution

By multiplying the mass of the solution (1kg = 1000g) by its density (1.83 g/mL), the volume of the acid solution in mL can be found. To get the volume in liters (for molarity), this value should be divided by 1000.
04

Calculation of the molarity

With both the moles of solute and volume of solution from steps 1 and 3, molarity can be calculated using the formula: \[ Molarity (M) = \frac {moles of solute} {volume of solution (in L)} \]

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Most popular questions from this chapter

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