# Heat Problem Set: Heat Capacity of Water

1. The air temperature above coastal areas is profoundly influenced by the large specific heat capacity of water. How large of a volume of air can be cooled by 1.0 C if energy is transferred as heat from the air to the water, thus increasing the temperature of 1.0 kg of water by 1.0 C? The specific heat capacity of air is approximately 1000.0 J/kg *C, and the density of air is approximately 1.29 kg/m^3.

2. Liquid nitrogen, which has a boiling point of 77 K, is commonly used to cool substances to low temperatures. How much energy must be removed from 1.0 kg of gaseous nitrogen at 77 K for it to completely liquefy?

3. How much energy is needed to melt exactly 1000 aluminum cans, each with a mass of 14.0 g, for recycling? Assume an initial temperature of 26.4 C.

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#### Solution Preview

The heat lost by air will be equal to the heat absorbed by water.

We have, heat lost or absorbed,

q = m*c*dT

where m is the mass, c is the specific heat capacity and dT is the change in temperature (final temp-initial temp)

Here the change in temperature is 1C for both air and ...

#### Solution Summary

Solution contains calculations and answers.

A simple problem set of 10 simple, short first year problems.

4. The term proof is defined as twice the percent of volume of pure ethanol in solution. Thus a solution that is 95% ethanol by volume is 190 proof. What is the molarity of ethanol in a 92 proof ethanol water solution? (density of ethanol is .8g/cm3; mol. wt. of ethanol is 46).

6. Find the mass percent of CuSO4 in a solution whose density is 1.3g/mL and whose molarity is 1.22M.

8. When .800g of NH4NO3 was added to 150g of water in a cup, the temperature dropped by .413 degrees centigrade. The heat capacity of water is 4.18J/degree centigrade. Assume the specific heat of the solution equals that of pure water and the calorimiter is ideal. What is the molar heat of solution of solid NH4NO3?

9. At a given temp., you have a mixture of benzene (vapor pressure is 745 torr), and toluene (vapor pressure is 290 torr). The mole fraction of the benzene in the solution is .590. Assuming ideal behavior calculate the mole fraction of the toluene in the vapor above the solution.

11. You have a 10.4g mixture of sugar (C12H22O11) and table salt (NaCl). When this mixture is dissolved in 150g of water the freezing point is found to be -2.24 degrees centigrade. Calculate the percent by mass of sugar in the original mixture.

13. A 5.5 g sample of a compound is dissolved in 250g of benzene. The freezing point of this solution is 1.02 degrees centigrade below that of pure benzene. What is the molar mass of this compound? (Kt for benzene is 5.12degrees C/m).

14. If .455g of Thyroxine is dissolved in 10g of benzene, the freezing point of the solution is 5.144 degrees centigrade. Pure benzene freezes at 5.444 degrees centigrade and has a value for the molal freezing point depression constant Kt of 5.12 degrees centigrade/m. What is the molar mass of Thyroxine?

15. Knowing that delta H of vaporization for water is 40.7kj/mol, calculate P of vaporization of water at 37 degrees centigrade.

18. Calculate the molarity of a solution containing KCl and water whose osmotic pressure at 21 degrees centigrade is 100 torr. Assume complete dissociation of the salt.

19. A .2M solution of MgSO4 has an observed osmotic pressure of 7.8atm at 25 degrees centigrade. Determine the observed van't Hoff factor for the experiment.

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