Sure, I'd be happy to help explain the steps involved in solving this problem.
To find the final temperature of the water after all the ice melts, you need to consider the heat transfer between the ice and the water.
Here's how to approach the problem:
1. Calculate the heat absorbed or released by each component using the formula Q = m * C * ΔT, where Q is the heat energy, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
For the ice cubes:
Q_ice = m_ice * C_ice * ΔT_ice
For the water:
Q_water = m_water * C_water * ΔT_water
2. Calculate the heat absorbed or released during the phase change of the ice. This is called the heat of fusion and is given by the formula Q_fusion = m_ice * ΔH_fusion.
3. Since the system is isolated (no energy is transferred to or from the surroundings), the heat lost by the water when the ice cools down is equal to the heat gained by the ice to melt. So, we can set up the equation:
Q_water + Q_fusion = Q_ice
4. Rearrange the equation to solve for the final temperature of the water (ΔT_water):
ΔT_water = (Q_ice - Q_fusion) / (m_water * C_water)
5. Plug in the given values into the appropriate equations:
m_ice = 20.0 g
ΔT_ice = 0 °C - (-10.0 °C) = 10.0 °C
m_water = 275 g
ΔT_water = ?
C_ice = 75.3 J/mol*K (since the enthalpy of fusion is given, it is for 1 mole of water, and the heat capacity is per mole as well)
C_water = 4.18 J/g*K (specific heat capacity of water)
ΔH_fusion = 6.01 kJ/mol = 6.01 × 10^3 J / (18.01528 g/mol) (conversion factor from kJ to J and gram to mole)
6. Substitute the given values into the equations and solve for the final temperature of the water.
I hope this explanation helps! If you have any more specific questions, feel free to ask.