A quantity of ice at 0.0 degrees C was added to 33.6 of water at 21.0 degree C to give water at 0.0 degrees C. How much ice was added? The heat of fusion of water is 6.01 kJ/mol and the specific heat is 4.18 J/(g * degrees C)


q = mass x specific heat x delta T?
q = mass x heat fusion?

I don't understand what to plug in
and where

heat removed from water in going from 21.0 to zero C is

mass x specific heat x delta T.
mass = 33.6 g
specific heat is 4.184 J/g*K
delta T is 21.0 - 0.

heat added to ice to melt it is
mass x heat fusion.
mass is the unknown.
heat fusion is given.
Note: you need to work in the same units. The heat of fusion is quoted in the problem in kJ/mol but I quoted the specific heat of water in J/gram. One needs to be changed. I would suggest the 4.184 be changed.

how much energy is required to melt 32.0 grams of ice (8.02 g/mol)?

To solve this problem, you need to use the principle of energy conservation. The heat gained by the ice (q1) must be equal to the heat lost by the water (q2), in order for the final temperature to be 0.0 degrees C.

We can calculate q1 using the equation:

q1 = mass of ice x specific heat capacity of ice x change in temperature

Since the ice is at 0.0 degrees C, the change in temperature is 0 degrees C.

Now, we need to calculate q2. The equation for q2 is:

q2 = mass of water x specific heat capacity of water x change in temperature

For the water, the change in temperature is (0.0 degrees C - 21.0 degrees C) = -21.0 degrees C.

Next, we know that q1 = -q2 because the heat lost by the water is equal to the heat gained by the ice. Therefore:

mass of ice x specific heat capacity of ice x 0 = mass of water x specific heat capacity of water x (-21.0 degrees C)

To solve for the mass of ice, we can rearrange the equation:

mass of ice = (mass of water x specific heat capacity of water x 21.0 degrees C) / specific heat capacity of ice

Now you can plug in the given values - mass of water = 33.6 g, specific heat capacity of water = 4.18 J/(g * degrees C), and specific heat capacity of ice = 2.01 kJ/(mol) = 2.01 J/(g * degrees C) - and solve for the mass of ice.

To solve this problem, we need to use the principle of conservation of energy.

First, let's calculate the heat transferred from the water to the ice. We can use the equation:

q1 = mass1 x specific heat1 x delta T1

Where:
- mass1 is the mass of water (33.6 g),
- specific heat1 is the specific heat of water (4.18 J/(g * °C)),
- delta T1 is the change in temperature of the water (0.0°C - 21.0°C = -21.0°C).

Substituting the values, we get:

q1 = 33.6 g x 4.18 J/(g * °C) x (-21.0°C)

Next, we need to calculate the heat absorbed by the ice to reach 0.0°C and then melt. We can use the equation:

q2 = mass2 x heat fusion

Where:
- mass2 is the mass of ice (what we're trying to find),
- heat fusion is the heat of fusion of water (6.01 kJ/mol).

For the heat of fusion, we need to convert it to J/g. Since 1 mole of water is equivalent to 18.015 g, we can calculate the heat fusion per gram:

heat fusion = 6.01 kJ/mol x (1000 J/1 kJ) / 18.015 g

Finally, the total heat transferred from the water to the ice should be equal to the heat absorbed by the ice:

q1 + q2 = 0

Solving for mass2, we can substitute the values and solve for it.

Note: The negative sign for delta T1 is because heat is being released by the water as it cools down.

I hope this helps explain how to approach this problem!