Question

How much energy is needed to change a 25.0 g ice cube at -10.0°C to steam at 110.0°C?

a) 3375 J
b) 6450 J
c) 9560 J
d) 12870 J

Answer 1

To calculate the energy needed, we need to consider heating the ice cube, melting the ice, and heating the water. The total energy required is 20480 J.

Step-by-step explanation:

To calculate the amount of energy needed to change the ice cube to steam, we need to consider the different phases and temperatures involved:

1. First, we need to calculate the energy required to heat the ice cube from -10.0°C to its melting point at 0.0°C. This is given by the equation:
   E1 = m * C * ΔT
   where m is the mass of the ice cube, C is the specific heat of ice, and ΔT is the change in temperature. Plugging in the values, we get:
   E1 = 25.0 g * 2.06 J/g°C * (0.0°C - (-10.0°C)) = 515 J
2. Next, we need to calculate the energy required to melt the ice cube at its melting point. This is given by the equation:
   E2 = m * ΔHf
   where ΔHf is the heat of fusion. For ice, ΔHf is 334 J/g. Plugging in the values, we get:
   E2 = 25.0 g * 334 J/g = 8350 J
3. Finally, we need to calculate the energy required to heat the water from its melting point to its boiling point and then to steam. This is given by the equation:
   E3 = m * C * ΔT
   where C is the specific heat of water and ΔT is the change in temperature. Plugging in the values, we get:
   E3 = 25.0 g * 4.18 J/g°C * (110.0°C - 0.0°C) = 11515 J

Adding up the energies required in each step, we get:
Total energy = E1 + E2 + E3 = 515 J + 8350 J + 11515 J = 20480 J

Therefore, the correct answer is 20480 J (not one of the given options).