Question

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

Answer 1

Answer:

102.6 g

Explanation:

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

$c=\frac{1}{2} M=0.5 M$

We're given the molar mass of:

$M=342 \frac{g}{mol}$

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

$c=\frac{n}{V}$

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

$n=\frac{m}{M}$

Substitute it back into the equation of molarity:

$c=\frac{n}{V}=\frac{\frac{m}{M} }{V}=\frac{m}{MV}$

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:

$600 cm^3 \cdot\frac{1 mL}{1 cm^3} \cdot \frac{1 L}{1000 mL} =0.600 L$

Substitute all three variables into the equation:

$m=0.5 M\cdot342 \frac{g}{mol}\cdot0.600 L=102.6 g$