How much energy, in calories, does it take to convert 20.0 grams of solid water, at 0.0 degrees C, into liquid water, at 0.0 degrees C? (The enthalpy of fusion for H2O is 1.44 kcal/mol)

rippp

To calculate the energy required to convert solid water (ice) to liquid water, we need to use the following formula:

Q = m * ΔH_fusion

Where:
Q is the energy required (in calories)
m is the mass of the substance (in grams)
ΔH_fusion is the enthalpy of fusion (in calories/gram)

In this case, the mass of the water is given as 20.0 grams and the enthalpy of fusion for water is 1.44 kcal/mol, or approximately 1.44 kcal/18 g (since the molar mass of water is approximately 18 g/mol).

First, let's calculate the energy required (Q):

Q = m * ΔH_fusion
= 20.0 g * (1.44 kcal / 18 g)

To cancel out the units, we divide the mass by 18 g:

Q = 20.0 g * (1.44 kcal/ 18 g)
= (20.0 g / 18 g) * 1.44 kcal
≈ 1.6 kcal

Therefore, it takes approximately 1.6 kilocalories (kcal) to convert 20.0 grams of solid water at 0.0 degrees Celsius into liquid water at 0.0 degrees Celsius.