Carbon dioxide $\mathrm{CO_2}$ is the gas that is mainly responsible for global warming (the greenhouse effect). The burning of fossil fuels is a major cause of the increased concentration of $\mathrm{CO_2}$ in the atmosphere. Carbon dioxide is also the end product of metabolism. Using glucose as an example of food, calculate the annual human production of $\mathrm{CO_2}$ in grams, assuming that each person consumes $5.0 X 10^2 g$ of glucose per day. The world's population is $7 .0$ billion, and there are $365$ days in a year.

Nitric oxide (NO) reacts with oxygen gas to form nitrogen dioxide $\left(\mathrm{NO}_2\right)$, a dark-brown gas:

$$2 \mathrm{NO}(g)+\mathrm{O}_2(g) \longrightarrow 2 \mathrm{NO}_2(g)$$

In one experiment, $0.886$ mole of $\mathrm{NO}$ is mixed with $0.503$ mole of $\mathrm{O}_2$. Determine which of the two reactants is the limiting reactant. Calculate also the number of moles of $\mathrm{NO}_2$ produced.

Cinnamic alcohol is used mainly in perfumery, particularly in soaps and cosmetics. Its molecular formula is $C_9H_{10}O$.
(a) Calculate the percent composition by mass of C, H, and O in cinnamic alcohol.
(b) How many molecules of cinnarnic alcohol are contained in a sample of mass $0.469 g$?

Consider the formation of nitrogen dioxide from nitric oxide and oxygen: 2 NO (g) + O2 (g) -> 2 NO2 (g) If 9.0 L of NO are reacted with excess O2 at STP, what is the volume in liters of the NO2 produced?

Nitrous oxide (N2O) the "laughing gas" used as an anesthetic by dentists, is made by thermal decomposition of solid NH4NO3. Write a balanced equation for this reaction. What are the oxidation states of N in NH4NO3 and in N2O?

Nitrous oxide

$$(\mathrm{N_2O})$$

is also called "laughing gas." It can be prepared by the thermal decomposition of ammonium nitrate

$$(\mathrm{NH_4NO_3}).$$

The other product is

$$\mathrm{H_2O}.$$

(a) Write a balanced equation for this reaction.

$$\\$$

(b) How many grams of

$$\mathrm{N_2O}$$

are formed if 0.46 mol of

$$\mathrm{NH_4NO_3}$$

is used in the reaction?

Balance the below-given equation using the method outlined in Section 8.1.

$$\text{$\mathrm{O}_3 \longrightarrow \mathrm{O}_2$}$$

The food flavor enhancer monosodium glutamate (MSG) has the composition 13.6% Na, $35.5 \% \mathrm{C}$, $4.8 \% \mathrm{H}, 8.3 \% \mathrm{~N}, 37.8 \% \mathrm{O}$, by mass. What is the empirical formula of MSG?

Evaluate the integral.

$$\int \frac { r ^ { 2 } } { r + 4 } d r$$

Evaluate the integral $\int\dfrac{r^2}{r + 4}~dr$.

One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron, is

$$\mathrm{Fe}_2 \mathrm{O}_3+3 \mathrm{CO} \longrightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_2$$

Suppose that $1.64 \times 10^3 \mathrm{~kg}$ of $\mathrm{Fe}$ are obtained from a $2.62 \times 10^3 \mathrm{~kg}$ sample of $\mathrm{Fe}_2 \mathrm{O}_3$. Assuming that the reaction goes to completion, what is the percent purity of $\mathrm{Fe}_2 \mathrm{O}_3$ in the original sample?

An impure sample of zinc $(\mathrm{Zn})$ is treated with an excess of sulfuric acid $\left(\mathrm{H}_2 \mathrm{SO}_4\right)$ to form zinc sulfate $\left(\mathrm{ZnSO}_4\right)$ and molecular hydrogen $\left(\mathrm{H}_2\right)$.
(a) Write a balanced equation for the reaction.
(b) If $0.0764 \mathrm{~g}$ of $\mathrm{H}_2$ is obtained from $3.86 \mathrm{~g}$ of the sample, calculate the percent purity of the sample.
(c) What assumptions must you make in (b)?

A certain metal oxide has the formula $\mathrm{MO}$, where $\mathrm{M}$ denotes the metal. A 39.46-g sample of the compound is strongly heated in an atmosphere of hydrogen to remove oxygen as water molecules. At the end, $31.70 \mathrm{~g}$ of the metal is left over. If $\mathrm{O}$ has an atomic mass of $16.00 \mathrm{amu}$, calculate the atomic mass of $\mathrm{M}$ and identify the element.

What is the molar mass of an atom? What are the commonly used units for molar mass?