Determine the melting point of an aqueous solution containing 115 mg of saccharin (C7H5O3NS)added to 1.00 mL of water (density of water=1.00 g/mL, Kt=1.86 C/m)
mols saccharin = 0.115g/molar mass
Solve for mols.
m = mols/kg solvent
m = mols/0.001
solve for m
delta T = Kf*m
Solve for delta T and subtract from 0 C to find the melting point.
Why did the saccharin want to know its melting point? It was feeling a bit "melty" and needed some solid advice! But, fear not, my friend. I'm here to help!
To find the melting point of this aqueous solution, we first need to calculate the molality (moles of solute per kilogram of solvent). We can use the following equation:
molality = (moles of solute) / (mass of solvent in kg)
First, let's convert the mass of saccharin to moles. The molar mass of saccharin is:
C: 12.01 g/mol
H: 1.01 g/mol
O: 16.00 g/mol
N: 14.01 g/mol
S: 32.07 g/mol
Now, let's calculate the moles of saccharin:
mass of saccharin = 115 mg = 0.115 g
moles of saccharin = (0.115 g) / (12.01 + 5 * 1.01 + 3 * 16.00 + 14.01 + 32.07) g/mol
Now that we have the moles of saccharin, we can calculate the molality. But since we were only given the volume of water, we need to convert that volume to mass using the density of water.
mass of water = (1.00 mL) * (1.00 g/mL) = 1.00 g
Finally, we can calculate the molality:
molality = (moles of saccharin) / (mass of water in kg)
Now that we have the molality, we can find the depression in the freezing point using the equation:
∆Tf = Kt × molality
where Kt is the cryoscopic constant (1.86 C/m).
But wait! The depression in the freezing point is equal to the difference between the freezing point of the solvent (water) and the freezing point of the solution. So, we need to add the freezing point of water (0 °C) to the depression in the freezing point to find the melting point of the solution.
Kindly note that this explanation is a humorously simplified version and may not contain all the technical details. Please consult a chemistry textbook or a real human chemist for more precise calculations.
To determine the melting point of the aqueous solution containing saccharin, we need to calculate the molality of the solution using the given information.
Step 1: Calculate the moles of saccharin added
Molecular weight of saccharin (C7H5O3NS) = (12.01 * 7) + (1.01 * 5) + (16.00 * 3) + 14.01 + 32.07 = 183.18 g/mol
Given mass of saccharin = 115 mg = 0.115 g
Moles of saccharin = mass / molecular weight = 0.115 g / 183.18 g/mol = 0.000628 mol
Step 2: Calculate the mass of water in kg
Volume of water = 1.00 mL = 0.001 L
Density of water = 1.00 g/mL
Mass of water = volume * density = 0.001 L * 1.00 g/mL = 0.001 kg
Step 3: Calculate the molality of the solution
Molality (m) = moles of solute / mass of solvent in kg
= 0.000628 mol / 0.001 kg
= 0.628 mol/kg
Step 4: Calculate the change in freezing point
Change in freezing point (ΔTf) = molality * Kt
= 0.628 mol/kg * 1.86 C/m
= 1.167 C
Step 5: Calculate the freezing point of the solution
Freezing point of pure water = 0 °C
Freezing point of the solution = Freezing point of pure water - ΔTf
= 0 °C - 1.167 C
= -1.167 C
Therefore, the melting point of the aqueous solution containing saccharin is -1.167 °C.
To determine the melting point of the aqueous solution containing saccharin, we need to calculate the molality of the solution and use the equation for freezing point depression.
1. Calculate the molality (m) of the solution.
Molality is defined as the number of moles of solute per kilogram of solvent.
The equation to calculate molality is:
molality (m) = moles of solute / mass of solvent (in kg)
First, we need to calculate the moles of saccharin.
Moles of saccharin = mass of saccharin / molar mass of saccharin
The molar mass of saccharin (C7H5O3NS) can be calculated as follows:
Molar mass of C = 12.01 g/mol
Molar mass of H = 1.01 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of N = 14.01 g/mol
Molar mass of S = 32.07 g/mol
Total molar mass of saccharin = (7 * 12.01) + (5 * 1.01) + (3 * 16.00) + 14.01 + 32.07
Next, convert the mass of water (1.00 mL) to kg.
mass of water = volume of water * density of water
mass of water = 1.00 mL * 1.00 g/mL
Finally, calculate the molality.
molality (m) = (moles of saccharin) / (mass of water in kg)
2. Use the equation for freezing point depression to calculate the change in freezing point (∆Tf).
The equation is given by:
∆Tf = Kt * m
where Kt is the cryoscopic constant (1.86 °C/m) and m is the molality calculated in step 1.
3. Calculate the freezing point of the solution.
The freezing point of the solution can be calculated using the equation:
Freezing point = Freezing point of pure solvent - ∆Tf
The freezing point of pure water is 0 °C.
By following these steps, you can calculate the freezing point of the aqueous solution containing saccharin.