Chemistry

Find free online Chemistry Topics covering a broad range of concepts from research institutes around the world.

Mixture of Gases – Dalton’s Law of Partial Pressure

Studies of non-reacting gaseous mixtures showed that in a gaseous mixture each component behaves independently. For a gaseous mixture, it is important to know, how the pressure of individual component contributes to the total pressure of the mixture.

John Dalton stated that “the total pressure of a mixture of non-reacting gases is the sum of partial pressures of the gases present in the mixture” where the partial pressure of a component gas is the pressure that it would exert if it were present alone in the same volume and temperature. This is known as Dalton’s law of partial pressures.

i.e., for a mixture containing three gases 1, 2 and 3 with partial pressures p₁, p₂ and p₃ in a container with volume V, the total pressure P_total will be give by

P_total = P₁ + P₂ + P₃ …………… (6.12)

Assuming that the gases behave ideally

The partial pressure can also be expressed as

Application of Dalton’s law

In a reaction involving the collection of gas by downward displacement of water, the pressure of dry vapor collected can be calculated using Dalton’s law.

P_{drygascollected} = P_total – P_{water vapour}

P_{water vapour} is generally referred as aqueous tension and its values are available for air at various temperatures.

Let us understand Dalton’s law by solving this problem. A mixture of gases contains 4.76 mole of Ne, 0.74 mole of Ar and 2.5 mole of Xe. Calculate the partial pressure of gases, if the total pressure is 2 atm at a fixed temperature.

Solution:

Graham’ s Law of Diffusion

Gases have a tendency to occupy all the available space. When two non-reactive gases are allowed to mix, the gas molecules migrate from region of higher concentration to a region of lower concentration. This property of gas which involves the movement of the gas molecules through another gases is called diffusion. Effusion is another process in which a gas escapes from a container through a very small hole.

Diffusion and Effusion of Gases

The rate of diffusion or effusion is inversely proportional to the square root of molar mass. This statement is called Graham’s law of diffusion/effusion.

Mathematically rate of diffusion α \(\frac{1}{\sqrt{\mathrm{M}}}\) Otherwise

where r_A and r_B are the rates of diffusion of A and B and the M_A and M_B are their respective molar masses.

Example:

1. An unknown gas diffuses at a rate of 0.5 time that of nitrogen at the same temperature and pressure. Calculate the molar mass of the unknown gas.

Solution:

Find free online Chemistry Topics covering a broad range of concepts from research institutes around the world.

Ideal Gas Equation

The gaseous state is described completely using the following four variables T, P, V and n and their relationships were governed by the gas laws studied so far.

Boyle’s law V α \(\frac{1}{P}\)
Charles law V α T
Avogadro’s law V α n

We can combine these equations into the following general equation that describes the physical behaviour of all gases.

V α \(\frac{nT}{P}\)

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

The above equation can be rearranged to give the ideal gas equation

PV = nRT …………………. (6.11)

We already know that pressure is expressed in many different units (Table 6.1) hence it is important to know the values of gas constant R in different units as well.

We can calculate R using the equation,

R = \(\frac{PV}{nT}\)

For Conditions in which P is 1 atm., volume 22.414 dm³ for 1 mole at 273.15 K.

Under standard conditions (STP) Where P = 1 bar (10⁵ pascal), V= 22.71 × 10^-3m³ for 1 mole
of a gas at 273.15 K

= 8.314 Pa m³K^-1mol^-1
= 8.314 × 10^-5bar m³K^-1mol^-1
= 8.314 × 10^-2bar dm³K^-1mol^-1
= 8.314 × 10^-2bar L K^-1mol^-1
= 8.314 J K^-1mol^-1

The ideal gas equation is a relationship between four variables (P, V, T, n). Since it describes the state of any gas, it is referred to as the equation of state of gases.

Let us calculate the pressure exerted by 2 moles of sulphur hexafluoride in a steel vessel of volume 6 dm³ at 70 °C assuming it is an ideal gas. We will use the ideal gas equation for this calculation as below:

= 9.39 atm.

The ideal gas law states that PV = NkT, where P is the absolute pressure of a gas, V is the volume it occupies, N is the number of atoms and molecules in the gas, and T is its absolute temperature.

In chemistry, the formula PV=nRT is the state equation for a hypothetical ideal gas. In the equation PV=nRT, the term “R” stands for the universal gas constant.

In SI units, p is measured in pascals, V is measured in cubic metres, n is measured in moles, and T in kelvins (the Kelvin scale is a shifted Celsius scale, where 0.00 K = -273.15 °C, the lowest possible temperature). R has the value 8.314 J/(K⋅mol) ≈ 2 cal/(K⋅mol), or 0.0821 L⋅atm/(mol⋅K).

It is the combination of Boyle’s law, Charles’s law and Avogadro’s law PV/T = constant the value of constant depends on for amount of gas and the units in which pressure and volume are measured. … (c) PV = nRT. PV =m/M × RT. The equation is called as an ideal gas equation.

Ideal Gas and Non-Ideal Gas Equation

Two types of gases exist. Real gas and Ideal gas. As the particle size of an ideal gas is extremely small and the mass is almost zero and no volume Ideal gas is also considered as a point mass. The molecules of real gas occupy space though they are small particles and also have volume.

The gas particles have negligible volume. The gas particles are equally sized and do not have intermolecular forces (attraction or repulsion) with other gas particles. The gas particles move randomly in agreement with Newton’s Laws of Motion. The gas particles have perfect elastic collisions with no energy loss. Ideal gases have mass and velocity.

Real Gas:

Real gases are defined as the gases that do not obey gas laws at all standard pressure and temperature.

The gas laws consist of three primary laws:

Charles’ Law, Boyle’s Law and Avogadro’s Law (all of which will later combine into the General Gas Equation and Ideal Gas Law).

An ideal gas is a gas whose pressure P, volume V, and temperature T are related by the ideal gas law: PV = nRT. where n is the number of moles of the gas and R is the ideal gas constant. Ideal gases are defined as having molecules of negligible size with an average molar kinetic energy dependent only on temperature.

Since the particles of an ideal gas have no volume, a gas should be able to be condensed to a volume of zero.

Reality Check:

Real gas particles occupy space. A gas will be condensed to form a liquid which has volume. The gas law no longer applies because the substance is no longer a gas.

Find free online Chemistry Topics covering a broad range of concepts from research institutes around the world.

The Gas Laws

The gas laws have played a major role in the development of chemistry. The physical properties of all gases are governed by the gas laws that were formulated based on the studies of the properties like pressure, volume, etc., as a function of temperature. Before studying the gas laws in detail, let us understand an important parameter, namely, the pressure.

Pressure is defined as force divided by the area to which the force is applied. The SI unit of pressure is pascal which is defined as 1 Newton per square meter (Nm^-2). There are other units that are commonly used and their relation with the SI unit is as follows.

Boyle’s Law: Pressure-Volume

Relationship

Robert Boyle performed a series of experiments to study the relation between the pressure and volume of gases. The schematic of the apparatus used by him is shown in figure 6.1.

Mercury was added through the open end of the apparatus such that the mercury level on both ends are equal as shown in the figure 6.1 (a). Add more amount of mercury until the volume of the trapped air is reduced to half of its original volume as shown in figure 6.1(b). The pressure exerted on the gas by the addition of excess mercury is given by the difference in mercury levels of the tube.

Initially the pressure exerted by the gas is equal to 1 atm as the difference in height of the mercury levels is zero. When the volume is reduced to half, the difference in mercury levels increases to 760 mm. Now the pressure exerted by the gas is equal to 2 atm. It led him to conclude that at a given temperature the volume occupied by a fixed mass of a gas is inversely proportional to its pressure.

Mathematically, the Boyle’s law can be written as

V α \(\frac{1}{P}\) ……………… (6.1)

(T and n are fixed, T-temperature, n- number of moles)

V = k × \(\frac{1}{P}\) ……………… (6.2)
k – proportionality constant
When we rearrange equation 6.2.

PV = k ………. (6.2a) (at constant temperature and mass)

Boyle’s law is applicable to all gases regardless of their chemical identity (provided the pressure is low). Therefore, for a given mass of a gas under two different sets of conditions at constant temperature we can write

P₁V₁ = P₂V₂ = K ………… (6.3)

P₁V₁ = P₂V₂ = k …………. (6.3)

The PV relationship can be understood as follows. The pressure is due to the force of the gas particles on the walls of the container. If a given amount of gas is compressed to half of its volume, the density is doubled and the number of particles hitting the unit area of the container will be doubled. Hence, the pressure would increase two fold.

Consequence of Boyle’s Law

The pressure-density relationship can be derived from the Boyle’s law as shown below.
P₁V₁ = P₂V₂ (Boyle’s law)
P₁\(\frac{m}{d₁}\) = P₂\(\frac{m}{d₂}\)

where “m” is the mass, d₁ and d₂ are the densities of gases at pressure P₁ and P₂ ………… (6.4)

In other words, the density of a gas is directly proportional to pressure.

In figure (6.3) let us find the missing parameters (volume in 6.3 (b) and pressure in 6.3 (c))

Solution:

According to Boyle’s law, at constant temperature for a given mass of gas at constant temperature,
P₁V₁ = P₂V₂ = P₃V₃
1 atm × 1 dm³ = 2 atm × V₂ = P₃ × 0.25 dm³

and P₃ × 0.25 dm³ = 1 atm × 1 dm³

Charles Law (Volume-temperature relationship)

The relationship between volume of a gas and its temperature was examined by J. A. C. Charles. He observed that for a fixed mass of a gas at constant pressure, the volume is directly proportional to its temperature (K). Mathematically it can be represented as (at constant P and n)
V = kT ………….. (6.5)
or \(\frac{V}{T}\) = Constant

If the temperature of the gas increases, the volume also increases in direct proportion, so that \(\frac{V}{T}\) is a constant. For the same system at constant pressure, one can write

\(\frac{\mathrm{V}_{1}}{\mathrm{~T}_{1}}=\frac{\mathrm{V}_{2}}{\mathrm{~T}_{2}}\) = Constant ………….. (6.6)

For example, if a balloon is moved from an ice cold water bath to a boiling water bath, the temperature of the gas increases. As a result, the gas molecules inside the balloon move faster and gas expands. Hence, the volume increases.

Variation of Volume with Temperature at Constant Pressure

The plot of the volume of the gas against its temperature at a given pressure is shown in the figure 6.5. From the graph it is clear that the volume of the gas linearly increases with temperature at a given pressure. Such lines are called isobars. It can be expressed by the following straight line equation.

V = mT + C where T is the temperature in degree Celsius and m & C are constants.

When T = 0ºC the volume becomes V₀ = C and slope of the straight line m is equal to ΔV/ΔT. Therefore the above equation can be written in the following form.

V = (\(\frac{∆V}{∆T}\))T + V₀ …………… (6.7) (n, P are constant)

Divide the equation 6.7 by V₀

Charles and Gay Lussac found that under constant pressure, the relative increase in volume per degree increase in temperature is same for all gases. The relative increase in volume per ºC (α) is equal to \(\frac{1}{V_{0}}\)(\(\frac{∆V}{∆T}\)).

Therefore

\(\frac{V}{V_{0}}\) = αT + 1
V = V₀(αT + 1) ………. (6.9)

Charles found that the coefficient of expansion is approximately equal to 1/273. It means that at constant pressure for a given mass, for each degree rise in temperature, all gases expand by 1/273 of their volume at 0ºC

If we extrapolate the straight line in the figure 6.5 beyond the experimental measurements, the straight line intersects the temperature axis (x-axis) at -273º C. This shows that the volume of the gas becomes zero at -273º C, more precisely this temperature is -273.15º C. Beyond this temperature the gas would have a negative volume which is physically impossible.

For this reason, this temperature was defined as absolute zero by Kelvin and he proposed a new temperature scale with absolute zero as starting point which is now called Kelvin scale. The only difference between the Kelvin scale of temperature and Celsius scale of temperature is that the zero position is shifted. The boiling and freezing point of water in both scales are given below.

Example:

In figure 6.6 let us find the missing parameters (volume in 6.6 (b) and temperature in 6.6(c))

Solution:

According to Charles law,

Gay-Lussac’s Law (Pressure Temperature Relationship)

Joseph Gay-Lussac stated that, at constant volume the pressure of a fixed mass of a gas is directly proportional to temperature. or \(\frac{P}{T}\) = Constant k

If P₁ and P₂ are the pressure at temperatures T₁ and T₂, respectively, then
from Gay Lussac’s law

Avogadro’s Hypothesis

Avogadro hypothesised that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules. The mathematical form of Avogadro’s hypothesis may be expressed as

V α n,
\(\frac{V_{1}}{n_{1}}=\frac{V_{2}}{n_{2}}\) = Constant ……….. (6.10)

where V₁ & n₁ are the volume and number of moles of a gas and V₂ & n₂ are a different set of values of volume and number of moles of the same gas at same temperature and pressure.

Find free online Chemistry Topics covering a broad range of concepts from research institutes around the world.

Introduction of Gaseous State

We can survive for weeks without food, days without water, but only minutes without air. Thus, we inhale a lungful of air every few seconds, keep some of the molecules for our own end, and some of the molecules that our body no longer needs, and exhale the mixture back into the surrounding air. The air around us is in the gaseous state, which is the simplest of the states of matter.

Although the chemical behaviour of gases depends on their composition, all the gases have remarkably similar physical behaviour. Earth is surrounded by an atmosphere of air whose composition in volume percentage is roughly 78 % nitrogen, 21 % oxygen and 1 % other gases. Of the known elements, only eleven are gases under normal atmospheric conditions. The elements hydrogen (H₂), nitrogen (N₂), oxygen (O₂), fluorine (F₂) and chlorine (Cl₂) exist as gaseous diatomic molecules.

Another form of oxygen, namely, ozone (O₃) is also a gas at room temperature. The noble gases, namely, helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe) and radon (Rn) of 18^th group are monatomic gases. Compounds such as carbon monoxide (CO), carbon dioxide (CO₂), nitrogen dioxide (NO₂) and nitric oxide (NO) also exist in gaseous state under normal atmospheric conditions. In this unit you will learn the properties of gases and other related phenomena.

Gaseous State is the simplest state of matter. In fact, the lowermost part of the atmosphere (called troposphere) in which we live is a mixture of gases like Dioxygen, Dinitrogen, Carbon Dioxide, Water Vapour etc.

The state of matter distinguished from the solid and liquid states by: relatively low density and viscosity; relatively great expansion and contraction with changes in pressure and temperature; the ability to diffuse readily; and the spontaneous tendency to become distributed uniformly throughout any container.

They do not have definite shape and take up the shape of the container. They do not possess definite volume due to weakest intermolecular forces. They are not rigid. They are easily compressible due to excess space between the particles of gas which compresses on applying pressure.

Gases have a lower density and are highly compressible as compared to solids and liquids. They exert an equal amount of pressure in all directions.
The space between gas particles is a lot, and they have high kinetic energy.

Gases have three characteristic properties:

1. They are easy to compress
2. They expand to fill their containers, and
3. They occupy far more space than the liquids or solids from which they form.

The gas constant is a physical constant denoted by R and is expressed in terms of units of energy per temperature increment per mole. It is also known as Ideal gas constant or molar gas constant or universal gas constant.

The density of gases are much larger than those of corresponding liquids. It is not a property of gases. Density is equal to mass divided volume. Since gases have larger volumes, their densities are lower than those corresponding to liquids.

Molecules within gases are further apart and weakly attracted to each other. Heat causes the molecules to move faster, (heat energy is converted to kinetic energy) which means that the volume of a gas increases more than the volume of a solid or liquid.

Find free online Chemistry Topics covering a broad range of concepts from research institutes around the world.

Biological Importance of Magnesium and Calcium

Magnesium and calcium also plays a vital role in biological functions. A typical adult human body contains about 25g of magnesium and 1200g of calcium. Magnesium plays an important role in many biochemical reactions catalysed by enzymes. It is the co-factor of all enzymes that utilize ATP in phosphate transfer and energy release.

It also essential for DNA synthesis and is responsible for the stability and proper functioning of DNA. It is also used for balancing electrolytes in our body. Deficiency of magnesium results into convulsion and neuromuscular irritation.

Calcium is a major component of bones and teeth. It is also present in in blood and its concentration is maintained by hormones (calcitonin and parathyroid hormone). Deficiency of calcium in blood causes it to take longer time to clot. It is also important for muscle contraction.

The main pigment that is responsible for photosynthesis, chlorophyll, contains magnesium which plays an important role in photosynthesis.

Calcium and Magnesium are alkaline earth metals, which have become a necessity in our everyday lives and elements which sustain the human body and help us function properly. These two elements are extremely effective alloy mediums and are used in different industries to serve various purposes.

Calcium ions (Ca²⁺) contribute to the physiology and biochemistry of organisms’ cells. They play an important role in signal transduction pathways, where they act as a second messenger, in neurotransmitter release from neurons, in contraction of all muscle cell types, and in fertilization.

Magnesium is needed for more than 300 biochemical reactions in the body. It helps to maintain normal  nerve and muscle function, supports a healthy immune system, keeps the heartbeat steady, and helps bones remain strong. It also helps adjust blood glucose levels. It aids in the production of energy and protein.

Biological significance of magnesium and calcium: Magnesium and calcium play an important role in the neuromuscular function and the intraneuronal transmission and blood coagulation. Magnesium also helps in maintaining the normal blood circulation in the human body.

Sodium is both an electrolyte and mineral. It helps keep the water (the amount of fluid inside and outside the body’s cells) and electrolyte balance of the body. Sodium is also important in how nerves and muscles work. Most of the sodium in the body (about 85%) is found in blood and lymph fluid.

Potassium is the main intracellular ion for all types of cells, while having a major role in maintenance of fluid and electrolyte balance. Potassium is necessary for the function of all living cells, and is thus present in all plant and animal tissues.

Magnesium is a nutrient that the body needs to stay healthy. Magnesium is important for many processes in the body, including regulating muscle and nerve function, blood sugar levels, and blood pressure and making protein, bone, and DNA.

Doses less than 350 mg daily are safe for most adults. In some people, magnesium might cause stomach upset, nausea, vomiting, diarrhea, and other side effects. When taken in very large amounts (greater than 350 mg daily), magnesium is POSSIBLY UNSAFE.

Magnesium keeps the immune system strong, helps strengthen muscles and bones, and supports many body functions from cardiac functions to brain functions. This is also a key hormone regulator for women. Low magnesium levels can contribute to PMS and menopausal symptoms.

They regulate the number of red and white blood corpuscles in the cell. (C) They can be present in any amount in the blood since they are absorbed by the cells. (D) They regulate the viscosity and color of the blood. Hint: Sodium and potassium ions both have different ability to penetrate the cell membrane.

Sodium maintains the electrolyte balance in the body. Potassium ions are primarily found inside the cell. Potassium ions maintain the osmolarity (the concentration of a solution expressed as the total number of solute particles per litre) of the cell. They also regulate the opening and the closing of the stomata.

Potassium and sodium are electrolytes that help your body maintain fluid and blood volume so it can function normally. However, consuming too little potassium and too much sodium can raise your blood pressure.

Function. The body uses sodium to control blood pressure and blood volume. Your body also needs sodium for your muscles and nerves to work properly.

Similar to sodium, potassium is critical to all living things, for the same reasons (i.e. it is used in the functioning of the nervous system, heart and the brain). The potassium ion is used extensively in intercellular fluids. Potassium plays an important role in the growth of plants.

These minerals are often found in ancient lake and sea beds. Caustic potash, another important source of potassium, is primarily mined in Germany, New Mexico, California and Utah. Pure potassium is a soft, waxy metal that can be easily cut with a knife.