Suppose you add a small ice cube to room temperature water in a coffee cup calorimeter. What is the final temperature when all the ice is melted? Assume that you have 200.0 mL of water at 25.0 degrees Celsius and the ice cube weighs 15.0 g and is at 0.0 degrees Celsius before being added to the water.

To find the final temperature when all the ice is melted, we can use the principle of conservation of energy.

The heat gained by the water in the coffee cup calorimeter is equal to the heat lost by the ice cube while melting.

First, let's calculate the heat gained by the water:

Q_water = m_water * C_water * ΔT_water

where:
m_water = mass of water = 200.0 g (since 1 mL of water is approximately 1 g)
C_water = specific heat capacity of water = 4.18 J/g°C (average value)
ΔT_water = change in temperature of water = final temperature - initial temperature
= T_final - 25.0°C

Next, let's calculate the heat lost by the ice cube:

Q_ice = m_ice * ΔH_fus

where:
m_ice = mass of ice = 15.0 g
ΔH_fus = enthalpy of fusion for ice = 333.5 J/g

According to the principle of conservation of energy, Q_water = Q_ice. Therefore:

m_water * C_water * ΔT_water = m_ice * ΔH_fus

Now, let's solve the equation for the final temperature, T_final:

T_final = (m_ice * ΔH_fus + m_water * C_water * 25.0°C) / (m_water * C_water)

Substituting the given values:

T_final = (15.0 g * 333.5 J/g + 200.0 g * 4.18 J/g°C * 25.0°C) / (200.0 g * 4.18 J/g°C)

Calculating the expression:

T_final = 5.02°C + 25.0°C

T_final = 30.02°C

Therefore, the final temperature when all the ice is melted is approximately 30.02°C.

heat lost in melting ice + heat gained by H2O from melted ice + heat lost by water @ 25C = 0

heat lost by melted ice = mass x heat fusion = 15 x heat fusion.

heat gained by H2O from ice = mass x specific heat H2O x (Tfinal-Tintial) = 15 x specific heat H2O x (Tfinal-0)

heat lost by 25C H2O = mass H2O x specific heat H2O x (Tfinal-Tinitial) = 200 x specific heat H2O x (Tfinal-25)

Now you put all of these together and solve for Tfinal.
[mass ice x heat fusion] + [mass H2O from ice x specific heat H2O x (Tfinal-Tinitial)] + [mass 25C H2O x specific heat H2O x (Tfinal-Tinitial)] = 0