# Chemistry gases

## Chemistry gases

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# Chemistry gases

# Chemistry

** **

- Molecular compounds are converted to gases much more easily than ionic compounds upon heating

- Molecular compounds usually boil at much lower temperatures than ionic compounds

- The stronger intermolecular forces, the less likely a compound can exist as a gas at ordinary temperatures

- Physical characteristics of gases:
- assume the volume and shape of their containers
- are the most compressible of the states of matter
- will mix evenly and completely when confined to the same

container

- have much lower densities than liquids and solids

__Pressure of a Gas:__

__ __

Gases exert pressure on any surface with which they come in contact, because gas molecules are constantly in motion.

SI unit: Pascal (Pa), defined as one Newton per square meter

Pressure = force/area 1 Pa = 1N/m^{2}

Atmospheric Pressure is the pressure exerted by the Earth’s atmosphere. The actual value of atmospheric pressure depends on location, temperature and weather conditions. The barometer measures atmospheric pressure. Standard atmospheric pressure (1 atm) is equal to the pressure that supports a column of mercury exactly 760 mm (or 76 cm) high at 0^{0}C at sea level. In other words, the standard atmosphere equals a pressure of 760 mmHg, where mmHg represents the pressure exerted by a column of mercury 1 mm high. The mmHg unit is also called the __torr__.

1 torr = 1 mmHg 1 atm = 760 mmHg = 760 torr

1 atm = 101 325 Pa 1 atm = 1.01325 x 10^{2} kPa

A manometer is a device used to measure the pressure of gases other than the atmosphere. Two types:

- closed tube – below atmospheric pressure
- open tube – equal to or greater than atmospheric pressure

Examples showing conversions from mmHg to atm and kPa:

** **

**THE GAS LAWS:**

** **

__The Pressure-Volume Relationship: Boyle’s Law__

As the pressure (P) is increased at a constant temperature (T), the volume (V) occupied by a given amount of gas decreases. There is an inverse relationship between volume and pressure of a gas at constant temperature. As the pressure increases, the volume decreases. Conversely, if the applied pressure is decreased, the volume the gas occupies increases.

__Boyle’s Law:__ the pressure of a fixed amount of gas at a constant temp is

inversely proportional to the volume of the gas

P is proportional to 1/V

P = k_{1} x 1/V (where k_{1} is the proportionality constant)

PV = k_{1}

The product of the pressure and volume of a gas at constant temperature and amount of gas is a constant.

Although the individual values of pressure and volume can vary greatly for a given sample of gas, as long as the temperature is held constant, and the amount of gas does not change, P x V is always equal to the same constant. For a given sample of gas under two different sets of conditions at constant temperature,

P_{1}V_{1} = k_{1} = P_{2}V_{2} or P_{1}V_{1} = P_{2}V_{2}

where V_{1} and V_{2} are the volumes at pressures P_{1} and P_{2} respectively.

__The Temp-Volume Relationship: Charles’s and Gay-Lussac’s Law__

__ __

At constant pressure, the volume of a gas sample expands when heated and contracts when cooled. At any given pressure, the plot of volume versus temperature yields a straight line. By extending the line to zero volume, we find the intercept on the temperature axis to be – 273.15^{0}C. At any other pressure, we get the same zero volume temperature intercept. We identify -273.15^{0}C as absolute zero, theoretically the lowest attainable temperature. An absolute temperature scale was set up, now called the Kelvin temp scale, with absolute zero as the starting point. On the Kelvin scale, 1 Kelvin is equal in magnitude to 1^{0}C. The only difference between the two scales is that the zero position is shifted.

The dependence of the volume of a gas on temperature is given by:

V is proportional to T

V = k_{2}T or V/T = k_{2} where k_{2} is the proportionality constant

__Charles Law:__ the volume of a fixed amount of gas maintained at constant

pressure is directly proportional to the absolute temperature of

the gas __ __

__ __

We can compare two sets of volume-temperature conditions for a given sample of gas at constant pressure.

V_{1}/T_{1} = k_{2} = V_{2}/T_{2} or V_{1}/T_{1} = V_{2}/T_{2}

where V_{1} and V_{2} are the volumes of the gas at temperatures T_{1} and T_{2} respectively.

Another form of Charles’s law shows that at constant amount of gas and volume, the pressure of a gas is proportional to temperature:

P is proportional to T P = k_{3}T or P/T = k_{3}

P_{1}/T_{1} = k_{3} = P_{2}/T_{2} or P_{1}/T_{1} = P_{2}/T_{2}

where P_{1} and P_{2} are the pressures of a gas at temperatures T_{1} and T_{2} respectively.

__The Volume-Amount Relationship: Avogadro’s Law__

__ __

At the same temperature and pressure, equal volumes of different gases contain the same number of molecules (or atoms, if the gas is monatomic). The volume of any gas must be proportional to the number of moles of molecules present. That is:

V is proportional to n V = k_{4}n

where n represents the number of moles and k_{4} is the proportionality constant

__Avogadro’s Law__: at constant pressure and temperature, the volume of a gas

is directly proportional to the number of moles of the gas

present

__The Ideal Gas Equation__

__ __

__Summary of the Gas Laws:__

__Boyle’s Law:__ V 1/P (at constant n and T)

__Charles’s Law:__ V T (at constant n and P)

__Avogadro’s Law:__ V n (at constant P and T)

We can combine all three expressions to form a single master equation for the behaviour of gases:

V nT/P = R nt/P or PV = nRT (The Ideal Gas Equation)

where R is the proportionality constant, called the gas constant.

The Ideal gas equation describes the relationship among the four variables P, V, T and n. An ideal gas is a hypothetical gas whose pressure-volume-temperature behaviour can be completely accounted for by the ideal gas equation.

R = 0.0821 L ·atm/K · mol

STP = standard temperature and pressure (0^{0}C and 1 atm)

The ideal gas equation is useful for problems that do not involve changes in P, V, and n for a gas sample. At times, we need to deal with changes in these variables. When conditions change, we use a modified form of the ideal gas equation that takes into account initial and final conditions.

P_{1}V_{1}/T_{1} = P_{2}V_{2}/T_{2}

before change = after change

n_{1} is usually equal to n_{2} because the amount of gas normally does not change

__Examples:__

__ __

- Calculate the pressure (in atm) exerted by 1.82 moles of the gas, SF
_{6}, in a steel vessel of volume 5.43 L at 69.5^{0}C.

- Calculate the volume (in L) occupied by 7.40 g of NH
_{3}at STP.

- An inflated helium balloon with a volume of 0.55 L at sea level (1.0 atm) is allowed to rise to a height of 6.5 km, where the pressure is about 0.40 atm. Assuming the temperature remains constant, what is the final volume of the balloon?

- A certain light bulb containing Ar at 1.20 atm and 18
^{0}C is heated to 85^{0}C at constant volume. Calculate its final pressure (in atm).

- A small bubble rises from the bottom of a lake, where T = 8
^{0}C and P = 6.4 atm, to the water’s surface, where T= 25^{0}C and P = 1.0 atm. Calculate the final volume (in mL) of the bubble if its initial volume was 2.1 mL.

*Source : http://www.horton.ednet.ns.ca/staff/coldwell/Chemistry%20(4%20folders%20-%20Anita)/AP%20CHEMISTRY/Gases,%20Liquids,%20&%20Solids/AP%20CHEMISTRY%20-%20Gases.doc*

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