The volume of a 2.50 M solution of hydrochloric acid required to prepare 2.0 liters of a 0.30 M solution has to be determined.
The concentration of a solution in terms of moles/liter is denoted by M. A 1 M solution has one mole of the solvent in one liter of the solution.
Two liters of 0.3 M hydrochloric acid solution contains 2*0.3 = 0.6 moles of hydrochloric acid. 1 liter of 2.5 M solution of the acid contains 2.5 moles of hydrochloric acid. If a volume V contains 0.6 moles `V*2.5 = 0.6 => V = 0.6/2.5 = 0.24` liters.
0.24 liter of 2.5 M solution of hydrochloric acid is needed to make 2 liters of 0.3 M solution.
The main equation for this problem is:
`M_1V_1 = M_2V_2`
M1/V1 is the initial molarity and volume, while M2/V2 is the final molarity and volume.
In your problem, you have been given values for M1, M2, and V2. You are looking for V1.
`(2.5M)V_1 = (0.30M)(2.0L)`
Multiply M2 and V2, then divide by M1 to find your unknown.
`(2.5M)V_1 = 0.6`
`V_1 = 0.24L`
Your answer should be in two sig figs.