Calculate the heat absorbed when 46.0 g of ice at -10.0°C is converted to liquid water at 85.0 °C. The specific heat of ice is 2.03 J/g °C, the molar heat of fusion of ice is 6010 J/mol, and the specific heat of water is 4.18 J/g °C.
The heat is calculated by considering the three-step process of warming ice from -10.0 °C to 0.0 °C, melting the ice, and heating liquid water to 85.0 °C
Why did the ice go to therapy? Because it had a meltdown!
Let's break down the calculation step by step:
1. Warming ice from -10.0 °C to 0.0 °C:
The heat absorbed can be calculated using the formula:
q = m * c * ΔT, where q is the heat absorbed, m is the mass, c is the specific heat, and ΔT is the change in temperature.
q1 = (46.0 g) * (2.03 J/g °C) * (0.0 °C - (-10.0 °C))
= (46.0 g) * (2.03 J/g °C) * (10.0 °C)
≈ 933.8 J
2. Melting the ice:
The heat absorbed during the phase change (fusion) can be calculated using the formula:
q = n * ΔHf, where q is the heat absorbed, n is the number of moles, and ΔHf is the molar heat of fusion.
First, we need to calculate the number of moles of ice:
moles = mass / molar mass of ice
The molar mass of ice is approximately 18.015 g/mol (molar mass of water).
moles = (46.0 g) / (18.015 g/mol)
≈ 2.551 mol
Now we can calculate the heat absorbed during the phase change:
q2 = (2.551 mol) * (6010 J/mol)
≈ 15,341.51 J
3. Heating liquid water from 0.0 °C to 85.0 °C:
q3 = (46.0 g) * (4.18 J/g °C) * (85.0 °C - 0.0 °C)
≈ 17,848.2 J
Finally, to get the total heat absorbed, we add up the individual steps:
total heat absorbed = q1 + q2 + q3
≈ 933.8 J + 15,341.51 J + 17,848.2 J
≈ 34,123.51 J
So, the heat absorbed during this three-step process is approximately 34,123.51 J. That's enough to make the ice "melt" away!
Step 1: Calculate the heat absorbed to warm the ice from -10.0 °C to 0.0 °C.
Q1 = mass × specific heat × change in temperature
Q1 = 46.0 g × 2.03 J/g °C × (0.0 °C - (-10.0 °C))
Q1 = 46.0 g × 2.03 J/g °C × 10.0 °C
Q1 = 932.2 J
Step 2: Calculate the heat absorbed to melt the ice.
Q2 = moles of ice × molar heat of fusion
Q2 = (mass of ice / molar mass of ice) × molar heat of fusion
First, let's calculate the moles of ice:
moles of ice = mass of ice / molar mass of ice
The molar mass of water (H2O) is 18.02 g/mol.
mass of ice = 46.0 g
molar mass of ice = 18.02 g/mol
moles of ice = 46.0 g / 18.02 g/mol
moles of ice ≈ 2.55 mol
Now, let's calculate Q2:
Q2 = 2.55 mol × 6010 J/mol
Q2 ≈ 15335.5 J
Step 3: Calculate the heat absorbed to heat the liquid water from 0.0 °C to 85.0 °C.
Q3 = mass × specific heat × change in temperature
Q3 = 46.0 g × 4.18 J/g °C × (85.0 °C - 0.0 °C)
Q3 = 46.0 g × 4.18 J/g °C × 85.0 °C
Q3 = 16973.0 J
Now, let's calculate the total heat absorbed by summing up the three steps:
Total heat absorbed = Q1 + Q2 + Q3
Total heat absorbed = 932.2 J + 15335.5 J + 16973.0 J
Total heat absorbed ≈ 33240.7 J
Therefore, the heat absorbed when 46.0 g of ice at -10.0°C is converted to liquid water at 85.0 °C is approximately 33240.7 J.
To calculate the heat absorbed when 46.0 g of ice at -10.0°C is converted to liquid water at 85.0°C, we need to consider the three-step process mentioned in the question: warming the ice from -10.0°C to 0.0°C, melting the ice, and heating the liquid water to 85.0°C.
Step 1: Warming the ice from -10.0°C to 0.0°C
To calculate the heat absorbed during this step, we will use the specific heat capacity of ice (2.03 J/g °C) and assume that the mass of ice remains constant.
Q1 = mass × specific heat capacity × change in temperature
Q1 = 46.0 g × 2.03 J/g °C × (0.0°C - (-10.0°C))
Step 2: Melting the ice
To calculate the heat absorbed during the melting process, we will use the molar heat of fusion of ice (6010 J/mol) and the molar mass of water (18.015 g/mol).
Q2 = mass × molar heat of fusion / molar mass of water
Q2 = 46.0 g × (6010 J/mol / 18.015 g/mol)
Step 3: Heating the liquid water to 85.0°C
To calculate the heat absorbed during this step, we will use the specific heat capacity of water (4.18 J/g °C) and again assume that the mass remains constant.
Q3 = mass × specific heat capacity × change in temperature
Q3 = 46.0 g × 4.18 J/g °C × (85.0°C - 0.0°C)
Finally, we can add up the heat absorbed in each step to find the total heat absorbed:
Total heat absorbed = Q1 + Q2 + Q3
You can now substitute the values into the equations and calculate the total heat absorbed.