Question

For an ideal gas, which pair of variables are inversely proportional to each other if all factors remain constant

Answer 1

Answer:

• There are four variables that directly affect the kinetic theory of gases: pressure, temperature, volume and the number of moles. Each of these variables has a direct or inverse effect on the others. The relationship of the other states of matter (solids and liquids) is not as easily determined as it is for gases. Four scientists determined individual laws that governed the relationships. These laws are often put together to create the combined gas law where the unused variables are considered constant and drop out of the equation. Boyle’s law states that pressure (P) and volume (V) are inversely proportional. Charles’ law states that volume (V) and temperature (T) are directly proportional.

• Gay-Lussac’s law states that pressure (P) and temperature (T) are directly proportional. Avagadro’s law states that the amount (n) of a substance is directly proportional to the volume (V). The combined gas law is written as follows: P1V1/n1T1 = P2V2/n2T2. The combined gas law calculations are used when a gas is transferred from one set of conditions to another set of conditions.

• It is important to recognize the contribution of Lord Kelvin to the field of kinetics. Kelvin determined that the temperature in Celsius caused the relationships between the temperature and other variables was non-linear but was always proportional to a single constant. This constant, 273.15, is known as the Kelvin constant and should be added to the Celsius temperature before performing any calculations. It has been theorized that the lowest possible temperature is 0K or –273.15˚C. At this point, scientists have determined that there should be absolutely no kinetic energy within a system, therefore no movement, and therefore no energy at all. This condition will probably never be realized since the natural processes that work in kinetics are always trying to move away from this temperature and would ultimately transfer energy into a system without any, negating the whole idea.

• If gas is at a static condition (not being transferred from one set of conditions to another set of conditions) the ideal gas law must be used. It was found that the pressure times the volume divided by the amount of the gas times the temperature are always equal to the same value. This value was given the symbol R and is equal to 8.31 L kPa/K mol (or .082 L atm/K mol). If you are given three of the variables you can calculate the fourth using the constant. The ideal gas law is written as follows: PV=nRT.

• Dalton discovered that the amount of a gas in a container had a direct effect on the pressure. His experiments showed that as you transfer gases from separate containers into a single container caused the pressure to increase to the total pressure of all of the gases combined. It is important to ensure that all of the gas pressures are in the same unit and then they can simply be added together. Dalton’s law of partial pressure is written as follows: ΣPn as 0àn. To convert between units, the following relationships should be used: 1atm = 760torr = 760 mm Hg = 30 in Hg = 101.3 kPa = 1bar.

• Graham’s law shows that when the velocities of two gases are related at the same temperature (meaning that the gases have the same energy) that the lighter gas will be the faster gas while the heavier gas will be the slower gas. The mass can be determined by the atomic mass or gram formula mass (sum of the atomic masses) for a compound or molecule. Graham’s law comes from relating the two kinetic energy equations for the two gases, KE=½mv2. By resolving the equations and cancelling the variables that will cancel we get v2/v1 = √(m1/m2).

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Answer 2

Answer:

• Pressure, temperature, volume, and the number of moles are the four variables that directly affect the kinetic theory of gases. Each of these variables influences the others in a direct or inverse manner. The relationship between the other states of matter (solids and liquids) is more difficult to identify than the link between gases. Individual laws governing the interactions were discovered by four scientists. These laws are frequently combined to form the combined gas law, in which the unnecessary variables are treated as constants and are removed from the equation. Pressure (P) and volume (V) are inversely proportional, according to Boyle's law. Volume (V) and temperature (T) are directly related, according to Charles' law.
• Pressure (P) and temperature (T) are directly related, according to Gay-law. Lussac's The quantity (n) of a substance is directly proportional to its volume, according to Avagadro's law (V). P1V1/n1T1 = P2V2/n2T2 is the formula for the combined gas law. When a gas is transported from one set of conditions to another, the combined gas law calculations are utilised.
• It is critical to acknowledge Lord Kelvin's contribution to the field of kinetics. Kelvin discovered that the relationship between temperature and other variables was non-linear but always proportional to a single constant when measured in Celsius. The Kelvin constant, which is $273.15,$ should be added to the Celsius temperature before any calculations are performed. The lowest feasible temperature has been calculated to be 0K or –273.15 C. At this stage, scientists have determined that a system should have no kinetic energy, no movement, and thus no energy. This situation will almost certainly never be attained because natural kinetic processes are constantly attempting to move away from this temperature.
• The ideal gas law must be utilised when gas is in a static state (not being transported from one set of conditions to another). It was discovered that the pressure multiplied by the volume divided by the amount of gas multiplied by the temperature is always the same. This value is 8.31 L kPa/K mol (or.082 L atm/K mol) and is denoted by the letter R. If you know three of the variables, you can use the constant to figure out the fourth. PV=nRT is how the ideal gas law is written.
• Dalton realised that the volume of gas in a container affected the pressure directly. His studies revealed that transferring gases from different containers into a single container increased the pressure to the total pressure of all the gases combined. It's critical to make sure that all of the gas pressures are in the same unit before adding them together. The partial pressure law of Dalton is expressed as follows: 0àn as EPn.  The following relationships should be used to convert between units: The following relationships should be used: 1atm = 760torr = 760 mm Hg = 30 in Hg = 101.3 kPa = 1bar.
• When the velocity of two gases are related at the same temperature (meaning the gases have the same energy), Graham's law states that the lighter gas will be quicker and the heavier gas will be slower. The atomic mass or gramme formula mass (sum of the atomic masses) of a chemical or molecule can be used to calculate its mass. Graham's law is derived from the KE=1/2mv2 relationship between the two kinetic energy equations for the two gases. We get v2/v1 = (m1/m2) by resolving the equations and cancelling the variables that will cancel.

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