# At 25 degree Celsius, 190 grams of glucose is dissolved in 1000 grams of water. For this solution which of the following is correct ? a. M=m b. M > m c. M < m d. M is independent of m

Jun 1, 2018

The correct answer is c. $M < m$.

#### Explanation:

Calculate the molal concentration of glucose

n_text(glucose) = 190 color(red)(cancel(color(black)("g glucose"))) ×"1 mol glucose"/(180.16 color(red)(cancel(color(black)("g glucose")))) = "1.054 mol glucose"

$m = \text{1.054 mol"/"1.000 kg" = "1.054 mol/kg}$

Calculate the molar concentration of glucose

We need the density of the solution to calculate its volume.

The density will be greater than that of water, say, 1.06 g/mL.

The mass of the solution is (190 + 1000) g = 1190 g. Then

V = 1190 color(red)(cancel(color(black)("g"))) × "1 mL"/(1.06 color(red)(cancel(color(black)("g")))) = "1120 mL = 1.12 L"

$M = \text{1.054 mol"/"1.12 L" = "0.985 mol/L}$

Conclusion: The moles per kilogram of solvent are usually greater than the moles per litre of solution because the solute increases the volume to more than one litre.

Statements a. and b. are incorrect.

The correct statement is c. $M < m$.

As $m$ changes, $M$ changes, so they are not independent of each other.

Option d. is therefore incorrect.