A 0.97 m aqueous solution of an ionic compound with the formula MX has a freezing point of -2.5 ∘C .
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I'm sorry the reast says to calculate the van't Hoff factor (i) for MX at this concentration.
To find the formula of the compound MX, we can use the freezing point depression equation.
Freezing point depression (ΔTf) is given by the formula:
ΔTf = Kf * molality
Where:
Kf is the cryoscopic constant (which is specific for the solvent used)
molality is the molal concentration of the solution
First, let's convert the freezing point from Celsius to Kelvin:
Tf(K) = Tf(°C) + 273.15
Tf(K) = -2.5 °C + 273.15
Tf(K) = 270.65 K
Next, we need to calculate the molality (m) of the solution. Molality is defined as the number of moles of solute per kilogram of solvent.
Since we are given the concentration of the solution in meters (m), which is the ratio of moles of solute to kilograms of solvent, we can directly use the given concentration.
Given that the solution has a concentration of 0.97 m, this means there are 0.97 moles of solute in 1 kilogram of solvent.
Now, let's plug in the values into the freezing point depression equation:
ΔTf = Kf * molality
Substituting the known values:
270.65 K = Kf * 0.97 m
Now, to find the formula of the ionic compound MX, we need to know the cryoscopic constant (Kf) specific for the solvent used. Without that information, we cannot determine the formula of the compound.
To determine the identity of the compound MX, we can use the concept of freezing point depression. Freezing point depression occurs when a solute (in this case, the compound MX) is added to a solvent (water) and lowers the freezing point of the resulting solution compared to the pure solvent.
In this case, we are given that the freezing point of the 0.97 m aqueous solution of MX is -2.5 ∘C. To find the identity of the compound MX, we need to calculate the van't Hoff factor (i), which is a measure of how many particles the solute breaks into when dissolved in the solvent.
The formula to calculate freezing point depression is:
∆Tf = i * Kf * m
Where:
∆Tf = Freezing point depression (change in freezing point)
i = van't Hoff factor
Kf = Cryoscopic constant (molal freezing point depression constant) of the solvent
m = molality of the solution (moles of solute per kilogram of solvent)
In this case, the Kf for water is 1.86 ∘C/m. We are given the molality of the solution as 0.97 m. So we can rearrange the formula to solve for i:
i = ∆Tf / (Kf * m)
Substituting the given values:
i = (-2.5 ∘C) / (1.86 ∘C/m * 0.97 m)
Simplifying the expression:
i ≈ -1.35
The van't Hoff factor (i) cannot be negative, so we should disregard the negative sign. The calculated value of i is approximately 1.35.
Since the value of i is close to 1, it suggests that the compound MX dissolves as individual particles (dissociates) in water, indicating that it is a non-ionic compound.
Therefore, based on the information given, the compound MX is likely a non-ionic compound dissolved in water.