making ice cream involves surrounding the ice cream canister with a bath of salt ice water. to get the mix of freeze at 7.00 C,how many grams of salt (NaCl;molar mass = 58) will you need to add to 3.5 kg of ice water bath? (Kf of water = 1.86C/m)
delta T = i*Kf*molality
You know delta T, i=2 (2 particles for NaCl), you know Kf, solve for molality.
Then molality = moles/kg solvent
Solve for moles.
Then moles = grams/molar mass.'
Solve for grams Nacl.
374 - 375 grams
381.99g
To find out how many grams of salt you will need to add to the ice water bath, you first need to determine the freezing point depression caused by the addition of salt.
The freezing point depression is determined by the formula:
ΔT = Kf * m
Where:
ΔT is the change in freezing point (in degrees Celsius)
Kf is the freezing point depression constant (in degrees Celsius per molal)
m is the molality of the solution (in mol/kg)
In this case, the freezing point change (ΔT) is given as 7.00°C, and the Kf value for water is 1.86°C/m.
To find the molality (m), you need to divide the moles of solute (salt) by the mass of the solvent (water) in kilograms.
First, convert the mass of the ice water bath from grams to kilograms:
3.5 kg = 3500 g
Next, calculate the mass of the solvent (water) in kilograms:
mass of water = mass of ice water bath - mass of solute (salt)
mass of water = 3500 g - mass of salt (unknown)
mass of water = 3500 g
Now, you can calculate the molality (m):
m = moles of solute (salt) / mass of water (kg)
To find the moles of salt, you can use the molar mass of NaCl:
molar mass of NaCl = 58 g/mol
moles of solute (salt) = mass of salt (g) / molar mass of NaCl
Since we have the mass of the ice water bath, but not yet the mass of salt, we will rearrange the equation to solve for the mass of salt:
mass of salt (g) = moles of solute (salt) * molar mass of NaCl
Let's plug in the values into the equations:
ΔT = Kf * m
7.00°C = 1.86°C/m * m
Now we can solve this equation to get the value of m (molality):
7.00/1.86 = m
m = 3.76 molal
Now, let's calculate the mass of salt:
moles of solute (salt) = mass of salt (g) / molar mass of NaCl
3.76 = mass of salt (g) / 58
From this, we can rearrange the equation to solve for the mass of salt:
mass of salt (g) = 3.76 molal * 58 g/mol
mass of salt (g) = 218.08 g
So, you will need to add approximately 218.08 grams of salt (NaCl) to the 3.5 kg of ice water bath to achieve a freezing point of 7.00°C.