States of Matter 1.10: The Ideal Gas Law Wiva k12 Chemistry

You have 15.0 L of nitrogen gas at 100°C and 200 kPa. What volume of gas will you have at STP?

1.) List givens. (What are you given?) P1 equals 200 kPaP1=200 kPa V1 equals 15.0 LV1=15.0 L T1 equals 100 squared C373 KT1=100οC(373 K) P2 equals 100 kPaP2=100 kPa T2 equals 273 KT2=273 K 2.) Identify what you are looking for. V2= ? 3.) Use the equation with all variables listed. Write the combined gas law equation. P1V1/T1=P2V2/T2 4.) Solve for the variable you seek. Solve for the unknown. V2=P1V1T2/T1P2 5.) Compute and check your answer. V2=(200 kPa)(15.0L)(273 K)(100 kPa)(373 K) Substitute known values. V2 equals 21.96 LV2=21.96 LRemember, temperatures must be in kelvins, so you have to convert 100°C to 373 K (K = °C + 273).

You have 15.0 L of nitrogen gas at 100°C100°C and 203 kPa. How many moles of nitrogen gas do you have?

1.) List the given values. P=203 kPa V equals 15.0 LV=15.0 L T equals 100 squared C373 KT=100οC(373 K) R equals 8.31L-kPa over mol-KR=8.31L-kPa/mol-K 2.) Identify what you are looking for. n= ? 3.) Use the equation with all variables listed. PV=nRT 4.) Solve for the variable you seek. n = PV / RTn=PVRT 5.) Compute and check your answer. Substitute the known values.Substitute the known values. n equals 203 kPa15.0 L over 8.31 L-kPa/mol-K373 Kn=(203 kPa)(15.0 L)(8.31 L-kPa/mol-K)(373 K) n equals 0.98 moln=0.98 mol Remember, temperatures must be in kelvins, so you have to convert 100°C to 373 K (K = °C + 273).

You can find the number of moles of a gas by using the ideal gas law.

Before the emergence of the ideal gas law, the only way to find the number of moles of a gas was to take the volume of gas at a given temperature and pressure, convert that volume to what it would be at STP, and divide by 22.4 L to get the number of moles. With the ideal gas law, though, you can find the number of moles of a gas under any temperature and pressure without converting to STP. Study the example on-screen.

The combined gas law and the ideal gas law simplify calculations.

Boyle's law, Charles's law, and Gay-Lussac's law can be combined into one equation, the combined gas law, PV/T = k or P1V1/T1 = P2V2/T2. Avogadro's law states that, at the same temperature and pressure, equal volumes of gases will contain the same number of atoms or molecules: V/n = k. All four of these gas laws are combined into the ideal gas law, PV = nRT or P1V1/T1n1 = P2V2/T2n2. Real gases and ideal gases behave similarly, except under low temperatures and high pressures.

Joseph-Louis Gay-Lussac publishes both Gay-Lussac's law, which describes the relationship between a gas's temperature and pressure, and Charles's law.

By combining all three of the gas laws, you can arrive at a combined gas law, as shown on-screen. This law incorporates Boyle's, Charles's, and Gay-Lussac's gas laws. This equation is useful, for example, for converting a known volume of gas at one temperature and pressure to an unknown volume at another temperature and pressure.

Boyle, Charles, and Gay-Lussac set the stage for unifying the gas laws.

Chemists Robert Boyle, Jacques Charles, and Joseph-Louis Gay-Lussac described the behavior of gases and discovered relationships between three parameters in a fixed amount of enclosed gas: pressure (P), volume (V), and temperature (T, in kelvins). -Boyle's law - at constant temperature, PV = k or P1V1 = P2V2 -Charles's law - at constant pressure, V = kT or V1/T1 = V2/T2 -Gay-Lussac's law - at constant volume, P = kT or P1/T1 = P2/T2 Each law considers two parameters with the third one constant. Can all three of these laws be combined into one relationship? Yes.

The ideal gas law emerged in the nineteenth century.

In 1834, French physicist and engineer Emile Clapeyron derived an equation that relates all four parameters of gases and combined the works of Boyle, Charles, Gay-Lussac, and Avogadro. The equation is called the ideal gas law. The most common form of the equation is PV = nRT where P is pressure, V is volume, n is number of moles, T is temperature in kelvins, and R is the ideal gas constant. In 1848, British physicist William Thomson (Lord Kelvin) derived the value of the gas constant. The SI value of R is 8.31 (L)(kPa)/(mol)(K). The ideal gas constant R when atmospheres (atm) are used instead of kilopascals is 0.0821 L-atm/mol-K.

One equation unifies the gas laws and describes gas behaviors.

In separate laws, Boyle, Charles, and Gay-Lussac described the behavior of the variables of a fixed amount of gas (pressure, volume, and temperature). Avogadro later introduced a fourth variable, the amount or moles of gas. Could these relationships be combined into one equation that describes the behavior of a gas? In this lesson, you will learn how these variables are combined into one ideal gas equation, or law, and how the ideal gas law can be used.

1787

Jacques Charles experiments and collects data leading to Charles's law, which describes the relationship between a gas's volume and temperature.

1802

Joseph-Louis Gay-Lussac publishes both Gay-Lussac's law, which describes the relationship between a gas's temperature and pressure, and Charles's law.

1834

Lord Kelvin and Emile Clapeyron develop and publish the ideal gas law. PV = nRT

What pressure is exerted by a 2.0 mol sample of gas in a 10.0 L container at 333 K?

P=553 kPa Remember, temperatures must be in kelvins, so you have to convert 100°C to 373 K (K = °C + 273).

ideal gas law

PV = nRT; the law uniting all four parameters of a gas

1662

Robert Boyle develops and publishes Boyle's law, which describes the relationship between a gas's volume and preSsure.

You can find the pressure of a quantity of gas by using the ideal gas law.

The ideal gas law allows you to calculate any parameter of a gas, given the other three parameters. It is widely used today in science and industry. What pressure is exerted by a 2.0 mol sample of gas in a 10.0 L container at 333 K?

Avogadro addressed the amount of gas.

The only assumption of the combined gas law is that you have an enclosed, fixed amount of gas. If we incorporate that assumption by adding some factor to deal with amount, we have a gas law that can be used under any conditions. Amedeo Avogadro proposed that, at the same temperature and pressure, equal volumes of gases contain an equal number of atoms or molecules. (One mole of any gas occupies 22.4 L.) He reasoned that in a volume of gas, the gas molecules are so far apart that most of the volume occupied by the gas is empty space. Therefore, it does not matter whether the gas molecules themselves are large or small. Mathematically, Avogadro's hypothesis is V/n = k where V is volume; n is number of moles; and k is a constant. Incorporating Avogadro's law into the combined gas law makes gas calculations even easier.

You can find the volume of a quantity of gas using the ideal gas law.

The volume of 0.75 mol of oxygen at 293 K and 75 kPa is 25 L. This volume can be calculated using the ideal gas law. What happens if the pressure is increased to 101.5 kPa?

Now review some model problems.

Turn to Problem Set 56, The Ideal Gas Law, in the Chemistry: Problems and Solutions book. Review the sample problems and complete problems 4-7. When you have finished, check your answers in the Solution Key.

What is the volume of 0.75 mol of oxygen at 293 K and 101.5 kPa?

V=18 L

Gases don't always behave in ideal ways.

What do we mean by an ideal gas? As you might expect, this is a kind of mental model of a gas that has ideal characteristics. Ideal gases are made of particles that occupy negligible volume. The particles are in constant random motion. All collisions between the particles and between the particles and the container walls are perfectly elastic. Elastic means that no energy is lost as heat or light during the collision. The particles do not interact with one another. For the most part, real gases do not behave this way. Their collisions are not elastic, they do occupy a significant volume, and they do have intermolecular forces.

The combined gas law makes gas calculations easier.

You have 15.0 L of nitrogen gas at 100°C and 200 kPa. What volume of gas will you have at STP? At one time, to solve this problem you would have had to apply both Boyle's law and Charles's law. First you would have used Boyle's law to convert the volume at 200 kPa to the volume at 100 kPa (at 373 K). Then you would have used Charles's law to convert the volume at 373 K to the volume at 273 K and 100 kPa (constant). Now you can solve this problem using only the combined gas law equation.

real gas

a gas as it actually behaves in all conditions of temperature and pressure

ideal gas constant

a mathematical value used in the ideal gas law and equal to 8.31 (L x kPa)/(K x mol).

ideal gas

an idealization of a gas as one that follows all gas laws exactly at all temperatures and pressures

Combined Gas Law

the law uniting temperature, pressure, and volume of a gas