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Chapter 2: Problem 12

A sample of oxygen gas at \(50^{\circ} \mathrm{C}\) is heated, reaching a final temperature of \(100^{\circ} \mathrm{C} .\) Which statement best describes the behavior of the gas molecules? (A) Their velocity increases by a factor of two. (B) Their velocity increases by a factor of four. (C) Their kinetic energy increases by a factor of 2. (D) Their kinetic energy increases by a factor of less than 2.

Short Answer

Expert verified
The best description of the behavior of the gas molecules is (D) Their kinetic energy increases by a factor of less than 2.

Step by step solution

01

Convert the temperatures to Kelvin

Oxygen's initial temperature is \(50^{\circ} \mathrm{C}\) and final temperature is \(100^{\circ} \mathrm{C}\). Temperature in Kelvin can be found by adding 273.15 to the temperature in Celsius. Initial temperature in Kelvin is \(50 + 273.15 = 323.15 \mathrm{K}\) and final temperature is \(100 + 273.15 = 373.15 \mathrm{K}\).
02

Calculate the ratio of final to initial temperature

The ratio of final to initial temperature is \( \frac{373.15}{323.15} = 1.155 \). This ratio represents the proportional increase in the kinetic energy of the gas molecules.
03

Determine the behavior of the gas molecules

The velocity of the gas molecules would be related to the square root of the kinetic energy, so \(\sqrt{1.155} = 1.075 \), which means the velocity of the gas molecules increased by a factor of less than two but the kinetic energy increased by the ratio of the temperatures, which is 1.155, a factor less than two.

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Most popular questions from this chapter

The enthalpy values for several reactions are as follows: (I) \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) \(\quad \Delta H=-131 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}\) (II) \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow 3 \mathrm{H}_{2}(g)+\mathrm{CO}(g)\) \(\quad \Delta H=206 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}\) (III) \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\) \(\quad \Delta H=-41 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}\) (IV) \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) \(\quad \Delta H=-890 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}\) In which of the reactions does the amount of energy released by the formation of bonds in the products exceed the amount of energy necessary to break the bonds of the reactants by the greatest amount? (A) Reaction I (B) Reaction II (C) Reaction III (D) Reaction IV

A compound is made up of entirely silicon and oxygen atoms. If there are 14.0 g of silicon and 32.0 g of oxygen present, what is the empirical formula of the compound? (A) \(\mathrm{SiO}_{2}\) (B) \(\mathrm{SiO}_{4}\) (C) \(\mathrm{Si}_{2} \mathrm{O}\) (D) \(\mathrm{Si}_{2} \mathrm{O}_{3}\)

Consider the Lewis structures for the following molecules: $$\begin{equation} \mathrm{CO}_{2}, \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{2}^{-}, \text {and } \mathrm{NO}_{3}^{-} \end{equation}$$ Which molecule would have the shortest bonds? (A) \(\mathrm{CO}_{2}\) (B) \(\mathrm{CO}_{3}^{2-}\) (C) \(\mathrm{NO}_{2}^{-}\) (D) \(\mathrm{NO}_{3}^{-}\)

A sample of \(\mathrm{H}_{2} \mathrm{S}\) gas is placed in an evacuated, sealed container and heated until the following decomposition reaction occurs at \(1000 \mathrm{K} :\) $$2 \mathrm{H}_{2} \mathrm{S}(g) \rightarrow 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \qquad K_{\mathrm{c}}=1.0 \times 10^{-6}$$ If, at a given point in the reaction, the value for the reaction quotient \(Q\) is determined to be \(2.5 \times 10^{-8},\) which of the following is occurring? (A) The concentration of the reactant is decreasing while the concentration of the products is increasing. (B) The concentration of the reactant is increasing while the concentration of the products is decreasing. (C) The system has passed the equilibrium point, and the concentration of all species involved in the reaction will remain constant. (D) The concentrations of all species involved are changing at the same rate.

Consider the Lewis structures for the following molecules: $$\begin{equation} \mathrm{CO}_{2}, \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{2}^{-}, \text {and } \mathrm{NO}_{3}^{-} \end{equation}$$ Which molecule would have the smallest bond angle between terminal atoms? (A) \(\mathrm{CO}_{2}\) (B) \(\mathrm{CO}_{3}^{2-}\) (C) \(\mathrm{NO}_{2}^{-}\) (D) \(\mathrm{NO}_{3}^{-}\)
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