Question

How much energy (in kilojoules) is needed to heat 5.40g of ice from -10.5∘C to 35.0∘C? The heat of fusion of water is 6.01kJ/mol, and the molar heat capacity is 36.6 J/(K⋅mol) for ice and 75.3 J/(K⋅mol) for liquid water.

Answer 1

Question #45771, Chemistry, Inorganic Chemistry

How much energy (in kilojoules) is needed to heat 5.40g of ice from -10.5°C to 35.0°C? The heat of fusion of water is 6.01kJ/mol, and the molar heat capacity is 36.6 J/(K·mol) for ice and 75.3 J/(K·mol) for liquid water.

Answer:

First, find out the number of moles of ice:

$$n = m / M = 5.4 / 18 = 0.3 \text{ mol}$$ $$M(H_2O) = 18 \text{ g/mol}$$

Then we can find the amount of heat that you need to pass the ice that he had started to float

$$n^*C_1^*dT_1 = H_1$$ $$H_1 = 0.3 * 36.6 * 10.5 = 115.29 \text{ (J)}$$

Now we find the energy that must be expended on the transition from the solid to the liquid substance:

$$H_2 = n^*H_{\text{phase tran}} = 0.3 * 6.01 = 1.80 \text{ (kJ)}$$

Further calculate how much energy you need to pass water for that would heat it from 0 degrees to 35.5:

$$H_3 = n^*C_2^*dT_2 = 0.3 * 75.3 * 35 = 790.65 \text{ (J)}$$

Than sum all H:

$$H = H_1 + H_2 + H_3 = 115.29 + 1800 + 790.65 = 2705.94 \text{ (J)}$$

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