Question

One teaspoon of sugar is dissolved in a cup of water at 25°C. A cup is 250 mL. You measure the density of the solution and find that it is equal to 1004.4 kg/m3. Assume a teaspoon of sugar is equal to 5 g and that sugar has the chemical formula of sucrose, given by C12H22O11.

a) What is the concentration of the solution in molal? The density of pure sucrose is 1590 kg/m3.
Hint: play close attention to the definition of molal.
b) You find out that the saturation of sucrose in water at 25°C is 2000 g/L.
i. How many teaspoons of sugar should be added to saturate 1 L of water?
ii. What is the mass% of the sucrose in solution at saturation?

Answer 1

Answer:

true

Explanation:

because true is true

Answer 2

The molal concentration of the solution will be $5.814$ × $10^{-5}$ mol/Kg, for 1L of water to be saturated 400 teaspoons must be added, and the mass percentage of sucrose in the solution at saturation will be 2%.

Given:

Temperature = 25°C

Volume = 250 mL = 0.25 L

The density of the solution = 1004.4 Kg/m³

1 teaspoon = 5g of sugar

To Find:

The concentration of the solution in molal.

The number of teaspoons of sugar should be added to saturate 1L of water.

The mass percentage of sucrose in solution at saturation.

Solution:

It's pretty simple to discover the answer to this question.

We know that,

A kilogram of a solvent has a total solute content of moles, which is called molality.

That is,

$Molality (m) = \frac{mol}{Kg}$

$Molality (m) = \frac{Number of moles of solute}{Kg of solvent}$

Firstly, we need to calculate the number of moles present in the solution,

For that,

$Number of moles = \frac{Given mass}{Molar mass}$

From the chemical formula of sucrose $(C_{12} H_{22} O_{11})$, the molar mass of sucrose is 342.3 g/mol.

On substituting the values,

$Number of moles = \frac{Given mass}{Molar mass}$

= $\frac{5}{342.3}$

= 0.0146

Then, we need to get the mass of solvent on Kg

For that we have,

$Density = \frac{Mass}{Volume}$

Therefore,

$Mass = Density$ × $Volume$

On substituting the given values,

Mass = 1004.4 × 0.25

= 251.1 Kg

Then, substitute the values of the number of moles and mass of solvent in Kg in the equation of molality.

That is,

$Molality (m) = \frac{Number of moles of solute}{Kg of solvent}$

= $\frac{0.0146}{251.1}$

= $5.814$ × $10^{-5}$ mol/Kg

Hence, the concentration of the solution will be equal to $5.814$ × $10^{-5}$ mol/Kg

It is given that,

The saturation of sucrose in water at 25°C is 2000g/L

Which means,

A sugar-water solution is considered saturated if it includes 1 liter of water and 2000 grams of sugar.

Therefore,

2000g of sucrose is used to saturate 1L of water

It is already given that,

5g of sucrose = 1 teaspoon

Therefore,

1g of sucrose = $\frac{1}{5}$ teaspoon

Then,

2000 g of sucrose = $\frac{1}{5}$ × $2000$ teaspoon

= 400 teaspoons

Hence, the number of teaspoons of sugar that should be added to saturate 1L of water will be 400.

We know that,

$Mass Percentage = \frac{Mass of solute}{Mass of solution}$  

By substituting the given values,

Mass % = $\frac{2000}{1000}$

Mass percentage = 2%

Hence, the mass percentage of the sucrose in solution at saturation will be 2%.

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