Liquid water is to be heated from to in an insulated tank containing of water (density )

CHEMISTRY · Multi-part · CBSE · Chemistry · Thermodynamics · Thermodynamics

Problem

Liquid water is to be heated from

20.0\,^{\circ}\text{C}

95.0\,^{\circ}\text{C}

in an insulated tank containing

250\,\text{L}

of water (density

1.00\,\text{g\,mL}^{-1}

). The only heat source is the reaction

\mathrm{2\,H_2(g)+O_2(g)\;\longrightarrow\;2\,H_2O(l)}

for which

\Delta H=-286\,\text{kJ\,mol}^{-1}

of water produced. Only

60\%

of the thermal energy released by the reaction is transferred to the water in the tank; the remainder is lost to the surroundings. Hydrogen gas will be supplied at

85^{\circ}\text{C}

and

1.20\,\text{atm}

. The universal gas constant may be taken as

R=0.0821\,\text{L\,atm\,mol}^{-1}\,\text{K}^{-1}

. Assume the molar heat capacity of liquid water is

4.18\,\text{J\,g}^{-1}\,^{\circ}\text{C}^{-1}

and remains constant over this temperature range. (a) Calculate the thermal energy, in kilojoules, required to raise the temperature of the water in the tank from

20.0\,^{\circ}\text{C}

95.0\,^{\circ}\text{C}

. (b) Determine the number of moles of liquid water that must be produced by the reaction so that, at

60\%

efficiency, the energy requirement found in part (a) is met. (c) Using the stoichiometry of the reaction, calculate the volume of hydrogen gas, in liters, that must react at

85^{\circ}\text{C}

and

1.20\,\text{atm}

to produce the amount of water found in part (b). (d) The tank operator claims that doubling the pressure of hydrogen while keeping the temperature fixed would halve the required volume of gas. Evaluate this claim quantitatively and explain whether it is correct.

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