It's January in Nashville and your local weather station just informed you that the temperature outside is -5.10 degrees Celsius. You estimate the amount of ice on your driveway to be approximately 30.0 kg. What is the minimum amount of sodium chloride in kilograms (kg) needed to lower the freezing point of the water so that the ice melts?
**Ignore the Van't Hoff Factor for this problem!
*Kf = 1.86 °C/m for water
*NaCl = 58.44 g/mol
2406.048 kg of NaCl
I am sorry. Right answer is 2406.048 g of NaCl
See https://www.jiskha.com/questions/124219/Its-January-in-Nashville-and-your-local-weather-station-just-informed-you-that-the
but note here you are to ignore the i factor of 2. You call that 1 in this problem.
To determine the minimum amount of sodium chloride (NaCl) needed to lower the freezing point of the water so that the ice melts, we can use the equation:
ΔT = Kf * m * i
Where:
ΔT is the change in freezing point of the water in degrees Celsius
Kf is the freezing point depression constant for water, which is 1.86 °C/m
m is the molality of the solution, which is the number of moles of solute per kilogram of solvent
i is the Van't Hoff factor, which accounts for the number of particles formed when the solute dissociates in the solvent.
In this case, since we are ignoring the Van't Hoff factor, we assume i to be 1.
First, we need to convert the given temperature from Celsius to Kelvin:
T = -5.10 °C + 273.15 = 268.05 K
Next, we need to calculate the molality (m) of the solution:
m = (moles of NaCl) / (mass of water in kg)
The moles of NaCl can be calculated using the molar mass of NaCl:
moles of NaCl = mass of NaCl / molar mass of NaCl
Given:
mass of NaCl = unknown
molar mass of NaCl = 58.44 g/mol
Now, we need to determine the mass of water in kg. Given that the estimated amount of ice on the driveway is 30.0 kg, we assume that the entire weight is due to water since ice is the solid form of water.
mass of water = 30.0 kg
Now we can solve for the mass of NaCl needed:
m = (mass of NaCl / 58.44 g/mol) / 30.0 kg
Simplifying further, we have:
m = (mass of NaCl / 58.44) / 30.0 kg
To isolate the mass of NaCl, we can rearrange the equation as follows:
mass of NaCl = m * 58.44 * 30.0 kg
Plugging in the given values, we can calculate the mass of NaCl needed to lower the freezing point:
mass of NaCl = (1.86 °C/m * 268.05 K * 58.44 g/mol) / 30.0 kg
mass of NaCl ≈ 3.55 g
Therefore, the minimum amount of sodium chloride needed to lower the freezing point of the water so that the ice melts is approximately 3.55 grams (g), which is equivalent to 0.00355 kilograms (kg).