Question

Find the mass of sucrose (molecular mass=342) required to be dissolved per 600cm² solution to prepare a semi molar solution.

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Answer 1

102.6 g

Step-by-step explanation:

Firstly, let's understand the terms used in the question. Semi-molar solution is a solution which has a molarity of:

`c=(1)/(2) M=0.5 M`

We're given the molar mass of:

`M=342 (g)/(mol)`

Let's use the definition of molarity: molarity is the ratio between the moles of solute and the volume of solution:

`c=(n)/(V)`

From here, we wish to express moles, n, as the ratio of mass of sucrose to its molar mass:

`n=(m)/(M)`

Substitute it back into the equation of molarity:

`c=(n)/(V)=((m)/(M) )/(V)=(m)/(MV)`

Since we wish to find mass, let's multiply both sides of the equation by MV to obtain mass equation:

`m=cMV`

Now, convert volume into liters knowing that 1 mL = 1 cm³ and 1000 mL = 1 L:

`600 cm^3 \cdot(1 mL)/(1 cm^3) \cdot (1 L)/(1000 mL) =0.600 L`

Substitute all three variables into the equation:

`m=0.5 M\cdot342 (g)/(mol)\cdot0.600 L=102.6 g`