Question

What is the concentration of sugar $\left( {{C_{12}}{H_{22}}{O_{11}}} \right)$ in $mol{L^{ - 1}}$ if its $20g$ are dissolve enough water to make a final volume up to $2L$.

Answer 1

We have to know that the concentration of sugar here means the molarity of the sugar. We have to calculate the molarity using the moles of solute and the volume of the solution. We can give the formula of molarity as,
$Molarity = \dfrac{{Moles Of Solute}}{{Volume Of Solution\left( {inL} \right)}}$

Complete answer:
We can define molarity as the amount of moles of solute per liter of the solution. We can represent molarity as $mol/L$ or $M$ and molarity is one of the most common units for measuring the solution’s concentration. We can write the equation for molarity as,
$Molarity = \dfrac{{Moles Of Solute}}{{Volume Of Solution\left( {inL} \right)}}$
In the given equation, the moles of solute are moles of the sugar and the volume of the solution is the volume of water.
We are provided with grams of sugar as $20g$ and the volume is $2L$. As the amount of sugar should be in grams, we have to convert the grams of sugar into moles of sugar using the molar mass.
Let us now calculate the moles of sugar as,
$Moles = \dfrac{{Grams}}{{Molarmass}}$
Substitute the grams of sugar in the above equation and the molar mass of sugar is $342.30g/mol$. The moles of sugar is,
$Moles = \dfrac{{Grams}}{{Molarmass}}$
Now we can substitute the known values we get,
$Moles = \dfrac{{20g}}{{342.3g/mol}}$
On simplification we get,
$Moles = 0.00584mol$
We have calculated the moles of sugar is $0.00584mol$.
Let us now calculate the molarity (concentration) of sugar using the moles of sugar and the volume of the solution.
The concentration of sugar is calculated as,
$Molarity = \dfrac{{Moles Of Solute}}{{Volume Of Solution\left( {inL} \right)}}$
Now we can substitute the known values we get,
$Molarity = \dfrac{{0.00584mol}}{{2L}}$
On simplification we get,
$Molarity = 0.00292\,mol/L$
The concentration of sugar when $20g$ of sugar is dissolved in $2L$ of water is $0.00292mol/L$.

Note:
We have to know that while calculating the molarity, we should convert the mass of solute (if given in grams) to moles of solute using the molar mass. If we don’t convert the grams of solute to moles of solute, then there would be an error in concentration. In case if the volume is given in any other unit than liters, the mentioned unit has to be converted into liters.