Question

calculating solubility & concentration practice:
the solubility of sugar in water at 20°c is 200g / 100 ml. how much sugar would be needed to make a saturated solution in 500 ml at 20 °c?
3 g of glucose is dissolved in 15 ml of water. what is the concentration in g/ml?
how many kg of salt needs to be added to 3 l of water to make a concentration of 100 g/l?

Explanation:

Step1: Calculate the mass of salt needed

The concentration formula is $C=\frac{m}{V}$, where $C$ is concentration, $m$ is mass and $V$ is volume. We want a concentration $C = 100\ g/L$ and volume $V=3\ L$. Rearranging the formula for $m$ gives $m = C\times V$.
$m=100\ g/L\times3\ L = 300\ g$. Convert grams to kilograms: $m = 300\ g\times\frac{1\ kg}{1000\ g}=0.3\ kg$.

Step2: Calculate the concentration of glucose solution

Given mass of glucose $m = 3\ g$ and volume of water $V = 15\ mL$. Using the concentration formula $C=\frac{m}{V}$.
$C=\frac{3\ g}{15\ mL}=0.2\ g/mL$.

Step3: Calculate the mass of sugar for saturated solution

The solubility of sugar is $200\ g/100\ mL$. For a volume $V = 500\ mL$, set up a proportion. If $\frac{200\ g}{100\ mL}=\frac{m}{500\ mL}$, then cross - multiply: $100\ mL\times m=200\ g\times500\ mL$. Solving for $m$ gives $m=\frac{200\ g\times500\ mL}{100\ mL}=1000\ g$.

Answer:

1. $0.3\ kg$ of salt is needed.
2. The concentration of the glucose solution is $0.2\ g/mL$.
3. $1000\ g$ of sugar is needed to make a saturated solution in $500\ mL$ at $20^{\circ}C$.