Question

Which of the following statements is(are) true? a. If the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant. b. If the temperature of a gas increases from 25 ' $\mathrm{C}$ to $50\mathrm{C},$ the volume of the gas would double, assuming that the pressure and the number of moles of gas remain constant. c. The device that measures atmospheric pressure is called a barometer. d. If the volume of a gas decreases by one-half, then the pressure would double, assuming that the number of moles and the temperature of the gas remain constant.

Short answer

Statements a, c, and d are true. Statement a is true because of Avogadro's Law (when the moles double, so does the volume at constant temperature and pressure). Statement c is true because a barometer measures atmospheric pressure. Statement d is true because of Boyle's Law (when the volume is halved, the pressure doubles at constant temperature and moles). Statement b is false because the volume does not double when the temperature increases from 25°C to 50°C, according to Charles's Law.

Step-by-step solution

Statement a: Moles doubled, volume doubled

This statement refers to Avogadro's Law, which states that for a gas at constant temperature and pressure, the volume is directly proportional to the number of moles (n) of the gas. Mathematically, this can be written as: $$V\propto n$$ If the number of moles of the gas is doubled (n → 2n), the volume will also double (V → 2V). Therefore, statement a is true.

Statement b: Temperature increases, volume doubles

This statement refers to Charles's Law, which states that for a gas at constant pressure and number of moles, the volume is directly proportional to the temperature (T) in Kelvin. Mathematically, this can be written as: $$V\propto T$$ However, the given temperatures are in Celsius. We must first convert them to Kelvin: $$\begin{gathered} T_1=25°C+273.15=298.15K \\ {T}_2=50°C+273.15=323.15K \end{gathered}$$ Now let's find the ratio of these temperatures: $$\frac{T_2}{T_1}=\frac{323.15}{298.15}=1.0839$$ This ratio is not equal to 2, so the volume does not double when the temperature increases from 25°C to 50°C, as given in the problem. Thus, statement b is false.

Statement c: Atmospheric pressure measurement

The statement claims that a barometer is the device used to measure atmospheric pressure. This statement is true, as a barometer is indeed an instrument used to measure atmospheric pressure.

Statement d: Volume halved, pressure doubled

This statement refers to Boyle's Law, which states that for a gas at constant temperature and number of moles, the volume (V) is inversely proportional to the pressure (P). Mathematically, this can be written as: $$PV=constant$$ If the volume of the gas decreases by one-half (V → V/2), then according to Boyle's Law, the pressure should double (P → 2P) for the product PV to remain constant. Therefore, statement d is true. In conclusion, statements a, c, and d are true, while statement b is false.

Key concepts

Avogadro's Law

Understanding Avogadro's Law is fundamental in grasping how gases behave under set conditions. This law shows a direct relationship between the number of gas molecules (in moles) and its volume. In simple terms, Avogadro's Law tells us that under the same temperature and pressure, more gas particles will occupy more space. Hence, if you double the amount of gas (while keeping temperature and pressure constant), the volume it occupies will also double. This behavior is essential when predicting how gases will expand or compress during reactions and processes.

To visualize this, consider a balloon being filled with helium. As you add more helium, which increases the number of moles, the balloon expands, demonstrating a larger volume — a perfect illustration of Avogadro's Law in action.

Charles's Law

Charles's Law is another crucial piece of the puzzle when understanding gas behavior. This principle addresses the relationship between a gas's volume and its temperature. When we maintain pressure and the number of gas particles constant, an increase in temperature will cause the gas to expand, meaning the volume will increase. Likewise, cooling the gas leads to a decrease in volume.

This can be seen on a hot day when the air inside a basketball can cause it to appear more inflated compared to a cold day. It’s because the air molecules move faster and take up more space when they are warmed. Remember, for accurate calculations, temperatures must always be in Kelvin since Charles's Law is based on absolute temperature.

Boyle's Law

Boyle's Law provides a clear explanation of how pressure and volume interact for a gas. It tells us that the volume of a gas will decrease as the pressure on it increases, if the temperature and number of moles of gas are held constant. Conversely, if the pressure drops, the volume rises.

An everyday example of Boyle's Law is using a syringe. As the plunger is pressed, the volume inside the chamber decreases, increasing the pressure, which can force liquid out of the syringe. This inverse relationship between pressure and volume is a fundamental concept for professions that deal with containing and manipulating gases, such as respiratory therapists and scuba divers.

Barometer Atmospheric Pressure

A barometer is an instrument designed to measure atmospheric pressure. Atmospheric pressure is the weight of air pressing down on the Earth and is vital to understand in various scientific fields, including meteorology and aviation. A classic mercury barometer consists of a glass tube filled with mercury inverted into a mercury-filled basin. Atmospheric pressure pushes against the mercury in the basin, changing the height of the mercury column in the glass tube.

Changes in atmospheric pressure can indicate weather changes; a rising barometer means high pressure and good weather, while a falling barometer is associated with low pressure and poor weather conditions. Barometers are essential for making forecasts and understanding how gases interact with the environment at different altitudes.