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Chapter 6: Problem 59

Determine the amount of heat (in kJ) given off when \(1.26 \times 10^{4} \mathrm{~g}\) of ammonia are produced according to the equation $$\begin{aligned}\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow & 2 \mathrm{NH}_{3}(g) \\ & \Delta H_{\mathrm{rxn}}^{\circ}=-92.6 \mathrm{~kJ} / \mathrm{mol} \end{aligned}$$ Assume that the reaction takes place under standardstate conditions at \(25^{\circ} \mathrm{C}\).

Short Answer

Expert verified
-34229 kJ

Step by step solution

01

Determine the Molar Mass of Ammonia

The molar mass of ammonia (NH_3) is \( 14.01 g/mol (for N) + 3(1.01 g/mol) (for H) = 17.04 g/mol \). This conversion factor will be used to convert the mass of ammonia to quantity in moles.
02

Convert Mass of Ammonia to Moles

Moles of ammonia can be calculated by dividing the given mass of ammonia by its molar mass. Therefore, \( (1.26 \times 10^4 g) \div 17.04 g/mol = 739.88 mol \) of ammonia.
03

Calculate the Heat Released

Now, since the enthalpy change for the formation of two moles of ammonia is given as -92.6 kJ, for one mole it would be half of this, i.e., -46.3 kJ. So for 739.88 moles of ammonia, the heat released would be \(-46.3 kJ/mol \times 739.88 mol = -34229 kJ\). The heat is negative, which means it is released.
04

Final Answer

To round things up, the total amount of heat given off when 1.26 x 10^4 g of ammonia are produced under the given conditions is approximately -34229 kJ. That is the amount of heat released during this chemical reaction.

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Most popular questions from this chapter

A quantity of \(2.00 \times 10^{2} \mathrm{~mL}\) of \(0.862 \mathrm{MHCl}\) is mixed with an equal volume of \(0.431 M \mathrm{Ba}(\mathrm{OH})_{2}\) in a constant-pressure calorimeter of negligible heat capacity. The initial temperature of the \(\mathrm{HCl}\) and \(\mathrm{Ba}(\mathrm{OH})_{2}\) solutions is the same at \(20.48^{\circ} \mathrm{C}\), For the process $$\mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)$$ the heat of neutralization is \(-56.2 \mathrm{~kJ} / \mathrm{mol}\). What is the final temperature of the mixed solution?

A 44.0-g sample of an unknown metal at \(99.0^{\circ} \mathrm{C}\) was placed in a constant-pressure calorimeter containing \(80.0 \mathrm{~g}\) of water at \(24.0^{\circ} \mathrm{C}\). The final temperature of the system was found to be \(28.4^{\circ} \mathrm{C}\). Calculate the specific heat of the metal. (The heat capacity of the calorimeter is \(\left.12.4 \mathrm{~J} /{ }^{\circ} \mathrm{C} .\right)\)

Explain what is meant by a state function. Give two examples of quantities that are state functions and two that are not.

\(\mathrm{Mg}^{2+}\) is a smaller cation than \(\mathrm{Na}^{+}\) and also carries more positive charge. Which of the two species has a larger hydration energy (in \(\mathrm{kJ} / \mathrm{mol}\) ) ? Explain.

Which of the following standard enthalpy of formation values is not zero at \(25^{\circ} \mathrm{C} ? \mathrm{Na}(s), \operatorname{Ne}(g)\) \(\mathrm{CH}_{4}(g), \mathrm{S}_{8}(s), \mathrm{Hg}(l), \mathrm{H}(g)\)
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