What is the concentration of sugar (C12H22O11) in mol L-1 if its 20 g are dissolved in enough water to make a final volume up to 2 L?

The correct option is 0.02925 mol L^-1.

To find the concentration (molarity) of the sugar solution, we follow a step-by-step process.

Step 1: Calculate the molar mass of sugar (C₁₂H₂₂O₁₁)
The chemical formula of sugar (sucrose) is C₁₂H₂₂O₁₁.
The atomic masses of the constituent elements are:
Carbon (C) = 12.011 g mol^-1
Hydrogen (H) = 1.008 g mol^-1
Oxygen (O) = 15.999 g mol^-1
Using these atomic masses, we calculate the molar mass as follows:

$$\text{Molar Mass of}{\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}=(12\times 12.011)+(22\times 1.008)+(11\times 15.999)$$

$$M=144.132+22.176+175.989=342.297\text{ g mol}{-}^1$$

For simplicity, we can use the approximate molar mass of sugar as 342.3 g mol^-1.

Step 2: Calculate the number of moles of sugar
The number of moles ($n$) is given by the formula:

$$n=\frac{\text{Mass of solute (g)}}{\text{Molar mass of solute (g mol}}$$

Given that the mass of sugar dissolved is 20 g:

$$n=\frac{20\text{ g}}{342.3\text{ g mol}{-}^1}\approx 0.05843\text{ mol}$$

Step 3: Calculate the molar concentration (molarity) of the solution
Molarity ($M$) is defined as the number of moles of solute dissolved per liter of solution:

$$\text{Molarity (M)}=\frac{\text{Moles of solute (mol)}}{\text{Volume of solution (L)}}$$

Given that the final volume of the solution is 2 L:

$$\text{Concentration}=\frac{0.05843\text{ mol}}{2\text{ L}}=0.029215\text{ mol L}{-}^1$$

Using standard atomic weights ($C=12$, $H=1$, $O=16$), the molar mass is exactly 342 g mol^-1, which gives:
$n=20/342=0.05848$ mol.
Dividing by 2 L yields:

$$\text{Concentration}=\frac{0.05848}{2}\approx 0.02924\text{ mol L}{-}^1$$

Rounding to the options provided, the closest and precise option matches 0.02925 mol L^-1.