When 0.5mol of a certain ionic substance is dissolved in 1.0kg of water, the freezing point of the resulting solution is -3.72 ∘ C .(Freezing point depression of water is -1.86 kgwater molsoluteparticles ). How many ions does the substance give when it dissolves?
To find out how many ions the substance gives when it dissolves, we need to determine the number of moles of the substance dissolved in the solution.
Given:
- Amount of substance dissolved (solvent): 1.0 kg of water
- Freezing point depression of water: -1.86 °C
- Freezing point of resulting solution: -3.72 °C
The freezing point depression is given by the equation:
ΔT = -K_f * m
where ΔT is the change in temperature of the solution, K_f is the molal freezing point depression constant for the solvent, and m is the molality of the solute (moles of solute particles per kilogram of solvent).
Rearranging the equation, we have:
m = ΔT / -K_f
Substituting the given values, we can calculate the molality (m):
m = (-3.72 °C) / (-1.86 °C kgmol^-1)
m = 2.0 mol kg^-1
Now, we can use the molality (m) to determine the number of moles of solute in the solution:
moles of solute = m * mass of solvent
moles of solute = 2.0 mol kg^-1 * 1.0 kg
moles of solute = 2.0 mol
Since the molar mass of the substance is not given, we cannot directly convert from moles to the number of ions. However, we can assume that the substance fully ionizes in water.
Therefore, for every mole of the substance dissolved, it will give the same number of ions in solution. Therefore, in this case, the substance gives 2 ions (assuming it fully ionizes) when it dissolves.