Question 14.3: Calculate the value of ΔU°rxn at 25°C for the reaction descr......

General Chemistry [1096620]

Calculate the value of $ΔU_{rxn}^{\circ}$ at 25°C for the reaction described by

2\ H_{2}(g) + O_{2}(g) → 2\ H_{2}O(l) \qquad ΔH_{rxn}^{\circ} = –571.6\ kJ·mol^{–1}

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

In this case, water is a liquid and so

\Delta v_{gas} = 0  –  (v_{H_{2}} + v_{O_{2}}) = 0  –  (2 + 1) = – 3

Thus at 25°C,

P\Delta V_{rxn}^{\circ} = \Delta v_{gas}RT = – 3RT = (–3)(8.3145\ J·mol^{–1}·K^{–1})(298\ K)= –7.43\ kJ·mol^{–1}

and, therefore, $ΔH_{rxn}^{\circ}$ and $ΔU_{rxn}^{\circ}$ differ by about $7\ kJ·mol^{–1}$ . We now use Equation 14.10 to calculate the value of $ΔU_{rxn}^{\circ}$ :

$ΔH_{rxn} = ΔU_{rxn} + P\Delta V_{rxn} \qquad (constant\ pressure)$ (14.10)

ΔU_{rxn}^{\circ} = ΔH_{rxn}^{\circ}  –  P\Delta V_{rxn}^{\circ} = –571.6\ kJ·mol^{–1}  –  (–7.43\ kJ·mol^{–1}) = –564.2\ kJ·mol^{–1}

Hence, in this case, the values of $ΔU_{rxn}^{\circ}$ and $ΔH_{rxn}^{\circ}$ differ by only about 1%; this will usually be the case.

Related Answered Questions

Question: 14.8

Use the ΔH°f data in Table 14.3 to calculate the value of ΔH°rxn for the combustion of ethanol, CH3CH2OH(l), at 25°C, described by the chemical equation CH3CH2OH(l) + 3 O2(g) → 2CO2(g) + 3 H2O(l) ...

Verified Answer:

Referring to Tables 14.2 and 14.3, we find that [l...

Question: 14.15

A 1.000-gram sample of octane, C8H18(l), is burned in a calorimeter like that shown in Figure 14.18, and the observed temperature increase is 1.679 K. The total heat capacity of the calorimeter is cV,cal = 28.46 kJ·K^–1 (where we write cV,cal to emphasize that the value of the heat capacity of the ...

Verified Answer:

(a) The equation for the combustion reaction is [l...

Question: 14.9

Chemical reactions can be used to produce flames for heating. The nonnuclear reaction with the highest attainable flame temperature (approximately 6000°C, about the surface temperature of the sun) is that between hydrogen and fluorine: H2(g) + F2(g) → 2HF(g) Use the molar bond enthalpies in ...

Verified Answer:

The reaction involves the breaking of one hydrogen...

Question: 14.1

How much work is required to compress a gas from a volume of 5.0 L to a volume of 2.5 L by exerting a constant pressure of 1.5 atm? ...

Verified Answer:

We use Equation 14.3:

w = –P\Delta V = –P(V...

Question: 14.14

A 0.500-L sample of 0.200 M NaCl(aq) is added to 0.500 L of 0.200 M AgNO3(aq) in a calorimeter with a known total heat capacity equal to 4.60 × 10³ J·K^−1 at a constant pressure of one bar. The observed temperature change is +1.423 K. Use these data to determine the value of ΔH°rxn for the equation ...

Verified Answer:

Stoichiometrically equivalent quantities of [latex...

Question: 14.13

A 50.0-gram piece of copper metal at 80.0°C is placed in 100.0 mL (100.0 g) of water at 10.0°C. Assuming no energy is lost to the surroundings as heat, what will be the final temperature of the copperwater system? Take the molar heat capacities of Cu(s) and H2O(l) as 24.4 J·mol^−1·°C^−1 and ...

Verified Answer:

When the hot copper metal is placed in the cool wa...

Question: 14.12

Calculate the specific heat of a sample of glass, given that the input of 150 joules of energy as heat to a 50.0-gram sample causes a temperature increase of 3.57°C. ...

Verified Answer:

Application of Equation 14.31 yields for the speci...

Question: 14.11

Calculate the energy as heat required to raise the temperature of 150 kg of water (40 gallons, the volume of a typical home water heater in the U.S.) from 18°C to 60°C, assuming no loss of energy to the surroundings. ...

Verified Answer:

The energy in the form of heat required can be cal...

Question: 14.10

When 4.219 kJ of energy are added as heat to 36.0 grams of water at one bar, the temperature of the water increases from 10.00°C to 38.05°C. Calculate the heat capacity of the 36.0 grams of H2O(l). ...

Verified Answer:

We use Equation 14.27. The value of ΔT is equal to...

Question: 14.2

Calculate the energy released as heat when 60.0 grams of iron(III) oxide, Fe2O3(s), is combined with 15.0 grams of Al(s) in the thermite reaction (Figure 14.7) at 25°C and a constant pressure of one bar. The equation for the reaction isFe2O3(s) + 2Al(s) → Al2O3(s) + 2Fe(s) ΔH°rxn = −851.5 kJ·mol^–1 ...

Verified Answer:

Because the masses of both reactants are given, we...