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Chapter 10: Problem 54

Consider the formation of nitrogen dioxide from nitric oxide and oxygen: $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) $$ If \(9.0 \mathrm{~L}\) of \(\mathrm{NO}\) is combined with excess \(\mathrm{O}_{2}\) at STP, what is the volume in liters of the \(\mathrm{NO}_{2}\) produced?

Short Answer

Expert verified
9.0 L of \(\mathrm{NO}_{2}\) is produced.

Step by step solution

01

Understand the Reaction at STP

The reaction given is \(2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\). Under standard temperature and pressure (STP) conditions, 1 mole of any gas occupies 22.4 L. This information will be essential for calculations in the next steps.
02

Convert Volume of NO to Moles

Using the molar volume at STP, convert the given volume of \(\mathrm{NO}\) to moles. Since \(1\) mole of a gas at STP equals \(22.4\) L, calculate the moles of \(\mathrm{NO}\) as follows:\[\text{moles of NO} = \frac{9.0 \text{ L}}{22.4 \text{ L/mol}} = 0.402 \text{ mol}\]
03

Use Stoichiometry to Find Moles of NO2

According to the balanced chemical equation, \(2\) moles of \(\mathrm{NO}\) produce \(2\) moles of \(\mathrm{NO}_{2}\). Therefore, the moles of \(\mathrm{NO}_{2}\) produced will be the same as the moles of \(\mathrm{NO}\). So, we have:\[0.402 \text{ mol of NO} \rightarrow 0.402 \text{ mol of NO}_{2}\]
04

Convert Moles of NO2 to Volume

Convert the moles of \(\mathrm{NO}_{2}\) back to volume using the molar volume at STP (22.4 L/mole):\[\text{Volume of NO}_{2} = 0.402 \text{ mol} \times 22.4 \text{ L/mol} = 9.0 \text{ L}\]
05

Conclusion

Since we performed the calculations correctly, the volume of \(\mathrm{NO}_{2}\) produced is equal to the initial volume of \(\mathrm{NO}\). Therefore, \(9.0\) L of \(\mathrm{NO}_{2}\) is produced.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Reactions
A chemical reaction involves the transformation of reactants into products. In our example, the reaction is between nitric oxide (NO) and oxygen (O extsubscript{2}), which forms nitrogen dioxide (NO extsubscript{2}). The balanced chemical equation is crucial to understanding the stoichiometry鈥攖he quantitative relationship between reactants and products. Here, the equation is \( 2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \). This tells us:
  • 2 moles of NO combine with 1 mole of O extsubscript{2} to produce 2 moles of NO extsubscript{2}.
  • The coefficients in the equation represent the ratio in which the chemicals react.
Understanding these ratios is critical for volume and mole calculations, which you'll use to determine how much product (NO extsubscript{2}) is formed.
Gas Laws
Gas laws describe how gases behave based on factors like volume, temperature, and pressure. A key concept is that the behavior of gases is predictable and follows certain principles:
  • At a constant temperature and pressure, the volume of a gas is directly proportional to the number of moles. This is known as Avogadro's Law.
  • Under standard temperature and pressure conditions (STP)鈥�0掳C (273 K) and 1 atm pressure鈥�1 mole of any ideal gas occupies a volume of 22.4 liters.
These principles are crucial for understanding the stoichiometric calculations that involve gases.
Mole Concept
The mole is a fundamental concept in chemistry that relates quantities on a macroscopic level to numbers of atoms or molecules. In this exercise, it's used to relate the mass of a substance to the volume of gases in a reaction:
  • A mole represents \( 6.022 \times 10^{23} \) entities (atoms, molecules, etc.).
  • Using the mole concept, we convert the volume of NO gas to moles using the molar volume at STP (22.4 L/mol).
This conversion helps in making predictions about the volume of product formed in the reaction, such as NO extsubscript{2} in our case.
STP
Standard Temperature and Pressure (STP) is a reference point used in chemistry to describe the conditions of a gas sample:
  • STP is defined as 0掳C (273 K) and 1 atm pressure.
  • These conditions allow us to use 22.4 liters as the volume of 1 mole of an ideal gas.
In this exercise, STP conditions simplify our calculations, allowing us to directly relate volumes and moles using the molar volume concept.
Volume Calculations
Volume calculations in stoichiometry involve using known values from a balanced chemical equation to find unknown quantities. We used this for the reaction:
  • First, we calculated the moles of NO given the volume (9.0 L) using the molar volume at STP (22.4 L/mol).
  • Next, we used stoichiometry to find moles of NO extsubscript{2}, matching the moles of NO.
  • Finally, we converted moles of NO extsubscript{2} back to volume, arriving again at 9.0 L.
This shows the conservation of volume under these reactions and conditions, emphasizing the importance of stoichiometry in predicting chemical reactions.

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Most popular questions from this chapter

The gas laws are vitally important to scuba divers. The pressure exerted by \(33 \mathrm{ft}\) of seawater is equivalent to 1 atm pressure. (a) A diver ascends quickly to the surface of the water from a depth of \(36 \mathrm{ft}\) without exhaling gas from his lungs. By what factor will the volume of his lungs increase by the time he reaches the surface? Assume that the temperature is constant. (b) The partial pressure of oxygen in air is about \(0.20 \mathrm{~atm}\). (Air is 20 percent oxygen by volume.) In deep-sea diving, the composition of air the diver breathes must be changed to maintain this partial pressure. What must the oxygen content (in percent by volume) be when the total pressure exerted on the diver is \(4.0 \mathrm{~atm} ?\) (At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gases.)

Which of the following statements is correct? (a) Heat is produced by the collision of gas molecules against one another. (b) When a gas is heated at constant volume, the molecules collide with one another more often.

Some ballpoint pens have a small hole in the main body of the pen. What is the purpose of this hole?

A \(5.00-\) mol sample of \(\mathrm{NH}_{3}\) gas is kept in a \(1.92-\mathrm{L}\) container at \(300 \mathrm{~K}\). If the van der Waals equation is assumed to give the correct answer for the pressure of the gas, calculate the percent error made in using the ideal gas equation to calculate the pressure.

Dry ice is solid carbon dioxide. A \(0.050-\mathrm{g}\) sample of dry ice is placed in an evacuated 4.6-L vessel at \(30^{\circ} \mathrm{C}\). Calculate the pressure inside the vessel after all the dry ice has been converted to \(\mathrm{CO}_{2}\) gas.
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