What is the molar change in enthalpy when 100g of ice is heated from -72°C to -18.2°C?(cp=37.4 J/k•mol)

Would the answer be 1118 kJ

I agree with the digits but not the decimal

Well, you're close, but not quite there. Let's do some calculations, shall we?

First, we need to find out how many moles of ice we have. We can use the molar mass of water, which is approximately 18 g/mol. So, we have 100 g of ice, which is 100/18 ≈ 5.56 moles.

Now, let's calculate the temperature change. We're going from -72°C to -18.2°C, so the change in temperature is -18.2 - (-72) = 53.8°C.

Next, we can calculate the molar change in enthalpy using the molar heat capacity formula: ΔH = c_p * n * ΔT, where cp is the molar heat capacity, n is the number of moles, and ΔT is the temperature change.

ΔH = 37.4 J/k∙mol * 5.56 mol * 53.8 °C = 11077.456 J

Now, we need to convert from joules to kilojoules, since the question asks for the answer in kJ.

11077.456 J = 11.077456 kJ

So, the molar change in enthalpy is approximately 11.1 kJ. Close, but not exactly 1118 kJ. Keep practicing, and remember, chemistry can be a balancing act, just like trying to balance on a unicycle while juggling flaming bowling pins.

To calculate the molar change in enthalpy, we need to follow these steps:

Step 1: Calculate the amount of heat needed to raise the temperature of the ice from -72°C to 0°C.
The specific heat capacity of ice (cp) is given as 37.4 J/k•mol.

Q1 = mass × specific heat capacity × temperature change

First, we need to convert the temperature change from Celsius to Kelvin:
ΔT1 = (-72°C to 0°C) = (-72 + 273.15 K to 0 + 273.15 K) = 201.15 K

Using the given mass of ice (100g), we can calculate Q1:

Q1 = 100g × 37.4 J/(K·mol) × 201.15 K = 752932 J

Step 2: Calculate the amount of heat needed to melt the ice at 0°C.
The molar enthalpy of fusion (ΔHfus) is the amount of heat needed to convert 1 mole of a substance from a solid to a liquid phase. For water, ΔHfus = 6.01 kJ/mol.

Q2 = moles × ΔHfus

First, we need to determine the number of moles of ice using its molar mass (18.015 g/mol):

moles = mass / molar mass = 100 g / 18.015 g/mol = 5.551 mol

Now, we can calculate Q2:

Q2 = 5.551 mol × (6.01 kJ/mol × 1000 J/1 kJ) = 33348.51 J

Step 3: Calculate the amount of heat needed to raise the temperature of the liquid water from 0°C to -18.2°C.
The specific heat capacity of water (cp) is given as 37.4 J/k•mol.

Q3 = mass × specific heat capacity × temperature change

Using the given mass of ice (100g), we can obtain Q3:

ΔT3 = (-18.2°C to 0°C) = (-18.2 + 273.15 K to 0 + 273.15 K) = 255.95 K

Q3 = 100g × 37.4 J/(K·mol) × 255.95 K = 954030 J

Step 4: Finally, we can calculate the total molar change in enthalpy (ΔH):

ΔH = Q1 + Q2 + Q3 = 752932 J + 33348.51 J + 954030 J = 1741310.51 J

Converting ΔH to kJ:

ΔH = 1741310.51 J × 1 kJ/1000 J = 1741.31051 kJ

Therefore, the molar change in enthalpy when 100g of ice is heated from -72°C to -18.2°C is approximately 1741.31051 kJ.

To calculate the molar change in enthalpy, we can use the formula:

ΔH = mcΔT

Where:
ΔH is the molar change in enthalpy (in J/mol)
m is the mass of the substance (in g)
c is the specific heat capacity (in J/(g*K))
ΔT is the change in temperature (in K or °C)

First, we need to calculate the change in temperature, which is ΔT = final temperature - initial temperature:

ΔT = -18.2°C - (-72°C) = 53.8°C

Since the specific heat capacity is given in J/(k•mol), we need to convert the mass of ice from grams to moles. To do this, we divide the mass by the molar mass of ice.

The molar mass of water (H2O) is approximately 18 g/mol. Therefore, the number of moles of ice is:

moles = mass / molar mass
moles = 100g / 18 g/mol ≈ 5.56 mol

Now we can calculate the molar change in enthalpy:

ΔH = mcΔT = (5.56 mol)(37.4 J/mol•K)(53.8 K)

ΔH ≈ 1118 kJ

So, you are correct. The molar change in enthalpy when 100g of ice is heated from -72°C to -18.2°C is approximately 1118 kJ.