7. In a certain experiment, a student
was provided with a container of
commercial sulphuric acid with the
following information on its label:
Molar mass = 98 g mol-1
, density
=1.804 g cm-3
, and purity = 98%.
The student was assigned to prepare
a 1 L of 0.2000 M dilute solution of
H2SO4 from the commercial bottle.
The student measured 10.00 cm3
of
concentrated acid and diluted it to
1000.00 cm3
.
(a) Calculate the molarity of the
acid solution prepared by the
student.
(b) What volume of concentrated
H2SO4 could be added to
the 10 cm3 to obtain exactly
0.2000 M of H2SO4 solution?
(a) To calculate the molarity of the acid solution prepared by the student, we first need to calculate the number of moles of H2SO4 in the 10.00 cm3 of concentrated acid.
Given:
Molar mass of H2SO4 = 98 g mol-1
Density of concentrated acid = 1.804 g cm-3
Purity of concentrated acid = 98%
To calculate the moles of H2SO4, we use the formula:
moles = mass / molar mass
The mass of the concentrated acid used is:
mass = volume x density
mass = 10.00 cm3 x 1.804 g cm-3
mass = 18.04 g
Since the purity of the concentrated acid is 98%, the mass of H2SO4 present is:
mass of H2SO4 = 0.98 x mass
mass of H2SO4 = 0.98 x 18.04 g
mass of H2SO4 = 17.6692 g
Now we can calculate the moles of H2SO4:
moles of H2SO4 = mass of H2SO4 / molar mass
moles of H2SO4 = 17.6692 g / 98 g mol-1
moles of H2SO4 ≈ 0.18035 mol
To calculate the molarity of the solution, we use the formula:
molarity = moles / volume
The volume of the solution prepared by the student is 1000.00 cm3 = 1 L, so:
molarity = 0.18035 mol / 1 L
molarity = 0.18035 M
Therefore, the molarity of the acid solution prepared by the student is 0.18035 M.
(b) To calculate the volume of concentrated H2SO4 that could be added to the 10 cm3 to obtain exactly 0.2000 M of H2SO4 solution, we need to use the formula:
M1V1 = M2V2
Where:
M1 = molarity of the concentrated H2SO4
V1 = volume of the concentrated H2SO4 added
M2 = desired molarity of the diluted H2SO4 solution
V2 = total volume of the diluted H2SO4 solution
We know that:
V1 = 10 cm3 (volume of the concentrated H2SO4 added)
M1 = ? (concentration of the concentrated H2SO4)
M2 = 0.2000 M (desired molarity of the diluted H2SO4 solution)
V2 = 1000.00 cm3 (total volume of the diluted H2SO4 solution)
Rearranging the equation, we can solve for M1:
M1 = (M2V2) / V1
M1 = (0.2000 M x 1000.00 cm3) / 10 cm3
M1 = 20 M
Therefore, the concentration of the concentrated H2SO4 needed to obtain a 0.2000 M solution is 20 M.
Note: It is important to note that a 20 M concentration is highly corrosive and should be handled with caution.