Question

The mass of glycerin (C3H8O3) , a nonelectrolyte , must be dissolved in 200.0 g water to give a solution with a freezing point of -1.5 c equal ....................... (kf= 1.86 ) ( h=1 , c=12 , o=16 )

a. - 14.1 g
b. - 15.8 g
c. - 14.5 g
d. 14.8g

Answer 1

The mass of glycerin
`(C_(3) H_(8) O_(3) )` , a nonelectrolyte , must be dissolved in 200.0 g water to give a solution with a freezing point of -1.5 c equal
`\[ \text{d. -14.8 g} \]` (kf= 1.86 ) ( h=1 , c=12 , o=16 )

Let's go through the calculations step by step:

1. Calculate the molality
`(\(m\))`:

`\[ m = (\Delta T_f)/(K_f) = (-1.5^\circ C)/(1.86 \, ^\circ C \cdot kg/mol) \approx -0.806 \, mol/kg \]\\`
2. Calculate the molar mass of glycerin
`(\(C_3H_8O_3\))`:

`\[ \text{Molar mass of glycerin} = 3 * \text{molar mass of C} + 8 * \text{molar mass of H} + 3 * \text{molar mass of O} \]\[ \text{Molar mass of glycerin} = 3 * 12 + 8 * 1 + 3 * 16 \, g/mol = 92 \, g/mol \]\\`
3. Determine the moles of glycerin using the molality:

`\[ \text{Moles} = m * \text{kg of solvent} = -0.806 \, mol/kg * 0.2 \, kg = -0.1612 \, mol \]`

4. Find the mass of glycerin using the moles and molar mass:

`\[ \text{Mass} = \text{Moles} * \text{Molar mass} = -0.1612 \, mol * 92 \, g/mol \approx -14.8 \, g \]\\`
So, the correct answer is:

`\[ \text{Mass of glycerin} \approx -14.8 \, g \]\\`
Therefore, the correct option is:

`\[ \text{d. -14.8 g} \]`

Answer 2

To find the mass of glycerin that must be dissolved in 200.0 g of water to give a solution with a freezing point of -1.5°C, use the formula for freezing point depression. The mass is approximately -14.86 g.

Step-by-step explanation:

To calculate the mass of glycerin (C3H8O3) needed to give a solution with a freezing point of -1.5°C, we can use the formula for freezing point depression:

ΔT = Kf * m

where ΔT is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution.

In this case, the change in freezing point (ΔT) is -1.5°C, and Kf is 1.86°C/m. Since glycerin is a nonelectrolyte, its molality is equal to its molarity.

Using the equation, we can solve for the molality:

-1.5 = 1.86 * m

m = -1.5 / 1.86

m ≈ -0.806 mol/kg

Now, we can calculate the moles of glycerin using the molality:

moles = m * kg of water

kg of water = 200.0 g / 1000 = 0.200 kg

moles = -0.806 * 0.200

moles ≈ -0.1612 mol

To convert moles to grams, we can use the molar mass of glycerin:

molar mass = (3 * 12.01) + (8 * 1.01) + (3 * 16.00)

molar mass ≈ 92.09 g/mol

mass = moles * molar mass

mass = -0.1612 * 92.09

mass ≈ -14.86 g

Therefore, the mass of glycerin (C3H8O3) that must be dissolved in 200.0 g of water to give a solution with a freezing point of -1.5°C is approximately -14.86 g.