# Which is the thickest solution-1(M) of syrup or 1(m) of syrup?

May 20, 2017

A 1 mol/L sucrose syrup is thicker (has a greater viscosity) than a 1 mol/kg solution.

#### Explanation:

We would predict that the more concentrated solution has the greater viscosity.

To confirm this, we must express both concentrations in the same units.

Convert a concentration of 1 mol/kg to a molarity.

The molar mass of sucrose (${\text{C"_12"H"_22"O}}_{11}$) is 342 g/mol.

A 1 mol/kg solution contains 342 g of sucrose in 1 kg of water.

The density ρ of the solution is 1.106 g/mL, so the volume is

V = 1342 color(red)(cancel(color(black)("g"))) × "1 mL"/(1.106 color(red)(cancel(color(black)("g")))) = "1213 mL" = "1.213 L"

$\text{Molarity" = "moles"/"litres" = "1 mol"/"1.213 L" = "0.824 mol/L}$

A 1 mol/kg solution of sucrose has a concentration of 0.824 mol/L.

Conclusion:

A 1 mol/L solution of sucrose is more concentrated than a 1 mol/kg solution, so it should be thicker.

(Confirmation: The viscosity of a 1 mol/kg solution is 2.52 times the viscosity of water, and the viscosity of a 1 mol/L solution is 3.26 times the viscosity of water.)