The molar heat of fusion for water is 6.01 kJ/mol. The heat capacity for water is 75 J/mol deg. Which expression gives the quantity of energy need to change 1.0 mol ice at 0C to liquid water at 25C?
A. 6010/(75x25)
B. 6.01+75
C. 6010+(75x25)
D. 6010/298+(75x25)
E. (6010+(75x25))/298
(mass ice x heat fusion) + (mass H2O x specific heat H2O x delta T) = ?
To calculate the amount of energy needed to change 1.0 mol of ice at 0°C to liquid water at 25°C, you need to consider two processes: the energy required to heat the ice from 0°C to 0°C (melting), and the energy required to heat the liquid water from 0°C to 25°C (heating).
First, let's calculate the energy required for the melting process using the molar heat of fusion. The molar heat of fusion for water is 6.01 kJ/mol. Since you have 1.0 mol of ice, the energy required for the melting process is:
Energy for melting = 6.01 kJ/mol
Next, let's calculate the energy required for the heating process. The heat capacity for water is 75 J/mol·°C. To heat 1.0 mol of water from 0°C to 25°C, the energy required is:
Energy for heating = (75 J/mol·°C) × (25°C - 0°C) = (75 J/mol·°C) × (25°C) = 1875 J/mol
Now, to calculate the total energy required, you need to add the energy for melting and the energy for heating:
Total energy required = Energy for melting + Energy for heating
Plugging in the values:
Total energy required = 6.01 kJ/mol + 1875 J/mol
To make the units consistent, convert kJ to J:
Total energy required = 6010 J/mol + 1875 J/mol
Combining the two terms:
Total energy required = 7885 J/mol
Therefore, the correct expression that gives the quantity of energy needed to change 1.0 mol ice at 0°C to liquid water at 25°C is:
C. 6010 + (75 × 25)