It's January in Nashville and your local weather station just informed you that the temperature outside is -8.9 degrees Celcius. You estimate the amount of ice on your driveway to be approximately 30kg. 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

delta T = i*Kf*m

delta T is 8.9.
i = 2 (because NaCl breaks into two ions)
Kf = 1.86 degrees/molal
calculate molality = m

molality = mols/kg solvent
You know molality, you know kg solvent, calculate mols.

mols = g/molar mass
you know mols from above, molar mass NaCl is about 58.5 (but you should get the exact number), calculate grams NaCl, then divide by 1000 to convert to kg NaCl.
Post your work if you get stuck.

I forgot to mention that the amount calculated this way will provide the kg NaCl to lower the freezing point of water to -8.9 degrees C at which point both ice and water can co-exist. It will take a smidgen more to make sure it all melts.

To calculate the minimum amount of sodium chloride (NaCl) needed to lower the freezing point of the ice and make it melt, we will use the concept of the freezing point depression. The formula to calculate the freezing point depression is:

ΔTf = Kf * i * m

Where:
ΔTf is the change in freezing point,
Kf is the cryoscopic constant,
i is the van't Hoff factor (which is the number of particles into which a compound dissociates in a solution),
m is the molality (moles of solute per kilogram of solvent).

In this case, we want to determine the amount of NaCl needed to decrease the freezing point so that ice will melt. The freezing point of pure water is 0 degrees Celsius. Using this information, we can calculate the change in freezing point (ΔTf) using the given temperature outside (-8.9 degrees Celsius).

ΔTf = 0 - (-8.9)
ΔTf = 8.9 degrees Celsius

Now, we need the cryoscopic constant (Kf) for water, which is 1.86 °C·kg/mol. The van't Hoff factor (i) for NaCl is 2 because NaCl dissociates into Na+ and Cl- ions when dissolved in water.

Next, we need to find the amount of water present on the driveway, which can be calculated using the density of water (approximately 1000 kg/m³, or 1 kg/L). Assuming that the density of ice is also 1000 kg/m³, we can calculate the volume of ice:

Volume = mass / density
Volume = 30 kg / 1000 kg/m³
Volume = 0.03 m³

Since the mass is given in kilograms, the volume will be in cubic meters.

Now we can calculate the number of moles of water in 0.03 m³ using the molar mass of water (18 g/mol):

moles = volume * density / molar mass
moles = 0.03 m³ * 1000 kg/m³ / 18 g/mol
moles = 1.667 mol

Next, we calculate the molality (m) by dividing the moles of solute (NaCl) by the mass of the solvent (water) in kilograms:

molality = moles of solute / mass of solvent (water in kg)
molality = ? / 1 kg

Now, rearranging the formula for ΔTf:

? = ΔTf / (Kf * i * m)
? = 8.9 / (1.86 * 2 * 1)
? = 2.396

Therefore, the minimum amount of sodium chloride (NaCl) needed to lower the freezing point of water so that the ice melts is approximately 2.396 kg.

To calculate the minimum amount of sodium chloride required to lower the freezing point of water, we need to determine the molality of the sodium chloride solution needed.

Molality is defined as the number of moles of solute (sodium chloride) per kilogram of solvent (water). The freezing point depression equation can be used to find the freezing point depression caused by the sodium chloride solution:

ΔT = Kf * m

where:
ΔT is the freezing point depression,
Kf is the cryoscopic constant for water (-1.86 °C·kg/mol), and
m is the molality of the solution.

First, convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = -8.9 + 273.15 = 264.25 K

Next, calculate the molality using the following formula:
m = moles of solute / mass of solvent (in kg)

Since the molality calculates the moles of solute per kilogram of solvent, we need to convert the mass of water into kilograms.

30 kg of ice = 30 kg of water (since ice and water have the same mass)

Now, calculate the number of moles of sodium chloride:
m = moles of NaCl / 30 kg

Rearranging the equation, we have:
moles of NaCl = m * 30 kg

Substitute the values into the equation:
moles of NaCl = ΔT / (Kf * m) * 30 kg

Since the goal is to find the minimum amount of sodium chloride needed, we want to calculate the moles needed to completely melt all the ice. This would occur when the freezing point depression is equal to the freezing point of water (0 °C).

ΔT = (0 - 264.25 K)

Substituting the values into the equation, we have:
moles of NaCl = (0 - 264.25 K) / (-1.86 °C·kg/mol * m) * 30 kg

By knowing the moles of NaCl, we can calculate the mass by multiplying it by the molar mass of sodium chloride (58.44 g/mol). Finally, divide the answer by 1000 to convert grams to kilograms:

mass of NaCl (kg) = (moles of NaCl) * (molar mass of NaCl) / 1000

Perform the calculations using the given data, and you will find the minimum amount of sodium chloride needed to lower the freezing point of water so that the ice melts.