Final answer:
To heat up 50.0g of ice at -20.0°C to its freezing point, melt it, and raise the temperature of the liquid to 50.0°C, a total of 180,684 J of heat is required. This is calculated by considering three steps: heating the ice to its melting point, melting the ice, and then heating the liquid water to its final temperature.
Step-by-step explanation:
To calculate the amount of heat required to heat up 50.0g of ice at -20.0°C to its freezing point, melt it, and raise the temperature of the liquid to 50.0°C, we need to consider three steps: heating the ice to its melting point, melting the ice, and then heating the liquid water to its final temperature.
Step 1: Heating the ice to its melting point:
Using the formula Q = mcΔT, where Q is the amount of heat, m is the mass, c is the specific heat capacity, and ΔT is the temperature change, we can calculate the heat required:
Q₁ = (mass of ice)(specific heat capacity of ice)(change in temperature)
Q₁ = (50.0g)(2.06 J/(g•°C))(0.00°C - (-20.0°C))
Q₁ = 2060 J
Step 2: Melting the ice:
Using the formula Q = mL, where Q is the amount of heat, m is the mass, and L is the heat of fusion, we can calculate the heat required:
Q₂ = (mass of ice)(heat of fusion)
Q₂ = (50.0g)(79.9 cal/g)(4.184 J/cal)
Q₂ = 167,204 J
Step 3: Heating the liquid water to the final temperature:
Using the formula Q = mcΔT, where Q is the amount of heat, m is the mass, c is the specific heat capacity of water, and ΔT is the temperature change, we can calculate the heat required:
Q₃ = (mass of water)(specific heat capacity of water)(change in temperature)
Q₃ = (50.0g)(4.184 J/(g•°C))(50.0°C - 0.00°C)
Q₃ = 10420 J
The total amount of heat required is the sum of Q₁, Q₂, and Q₃:
Total heat required = Q₁ + Q₂ + Q₃ = 2060 J + 167,204 J + 10420 J = 180,684 J