Equations combined gas

We will be solving the combined gas equation for V2, so we will take the combined gas law and rearrange for V2 ... 

In the combined gas equation, we held just the amount constant. If, however, we hold two quantities constant and look at the relationship between the other two we can derive the other common gas laws shown below in Table 5-1. 

If you have a gas at a certain set of volume/temperature/pressure conditions and at least some of the conditions change, then you will probably be using the combined gas equation. If moles of gas are involved, the ideal gas equation will probably be necessary... 

Write the rearranged expression of the combined gas equation where you are solving for T2. 

Now substitute the known quantities into the equation. (You could substitute the knowns into the combined gas equation first, and then solve for the volume. Do it whichever way is easier for you.)... 

In using the combined gas equation, make sure you group all initial-condition quantities on one side of the equals sign and all final-condition quantities on the other side. 

For example, air sampling of a compound is performed at an altitude where the temperature is 7°C and the pressure is 725 torr. Conversion of ppm (W/V) to mg/m3 can be calculated using either the combined gas equation or by the ideal gas equation as illustrated below. 

In this question the units are given in atmospheres, so we will answer it in the same units. The answer in standard units is given for completeness. Let s rearrange the combined gas equation to give P2 on the LHS and put these figures in. 

The combined gas equation gives you a way to calculate changes involving pressure, volume, and temperature. But you still have the problem of amount to deal with. In order to account for amount, you need to Imow another law. 

The ideal gas equation (and even the combined gas equation) allows chemists to work stoichiometry problems involving gases. (Chapter 10 is your key to the world of stoichiometry.) In this section, you re going to use the ideal gas equation to do such a problem, using a classic chemistry experiment — the decomposition of potassium chlorate to potassium chloride and oxygen by heating ... 

More often than not, the given and wanted gas volumes are at different temperatures and pressures. The convenient L (given) L (wanted) cannot be used—yet. First, you use the combined gas equation solved for V2 (see Section 14.1, Equation 4.20) to change the volume of the given gas from its initial temperature and pressure to what that volume would be at the temperature and pressure of the wanted gas. Then both gases are at the same temperature and pressure, and you can use the L (given) L (wanted) shortcut. 

Flow and Performance Calculations. Electro dynamic equations are usehil when local gas conditions (, a, B) are known. In order to describe the behavior of the dow as a whole, however, it is necessary to combine these equations with the appropriate dow conservation and state equations. These last are the mass, momentum, and energy conservation equations, an equation of state for the working duid, an expression for the electrical conductivity, and the generalized Ohm s law. 

Boyle s and Charles laws can he combined into the ideal gas equation ... 

The ideal gas equation can be combined with the mole-mass relation to find the molar mass of an unknown gas PV = nRT (ideal gas equation) and n — (mole-mass relation) if we know the pressure, volume, and temperature of a gas sample, we can use this information to calculate how many moles are... 

We can use the ideal gas equation to calculate the molar mass. Then we can use the molar mass to identify the correct molecular formula among a group of possible candidates, knowing that the products must contain the same elements as the reactants. The problem involves a chemical reaction, so we must make a connection between the gas measurements and the chemistry that takes place. Because the reactants and one product are known, we can write a partial equation that describes the chemical reaction CaC2(. ) +H2 0(/) Gas -I- OH" ((2 q) In any chemical reaction, atoms must be conserved, so the gas molecules can contain only H, O, C, and/or Ca atoms. To determine the chemical formula of the gas, we must find the combination of these elements that gives the observed molar mass. 

Whereas liquids and solids have well-defined densities, the density of a gas varies strongly with the conditions. To see this, we combine the ideal gas equation and the mole-mass relation and rearrange to obtain an equation for... 

As discussed earlier, the mean drift velocity is the volume flux, Jv [see Eq. (70)]. Using the ideal gas equation to relate volume flow to molar flow [see Eq. (71)], the relationship between mean drift velocity and molar flux J may be written as um = (RTIPa)J. With this expression for um, Eqs. (80) and (81) are combined to give the desired expression for molar flux,... 

Write an equation for the combined gas law using temperature in Celsius. Explain why the Kelvin scale is more convenient. 

B Here we are not dealing with gaseous reactants the law of combining volumes cannot be used. From the ideal gas equation we determine the amount of N2(g) per liter under the specified conditions. Then we determine the amount of Na(l) produced simultaneously, and finally the mass of that Na(l). 

It is possible to combine Avogadro s law and the combined gas law to produce the ideal gas equation, which incorporates the pressure, volume, temperature, and amount relationships of a gas. The ideal gas equation has the form of... 

We can use the gas law relationships, especially the ideal gas law and the combined gas law, in reaction stoichiometry problems. For example, suppose you have 2.50 g of an impure sample of KC103 and you want to determine how many grams of pure KC103 are present. You heat the mixture and the KC103 decomposes according to the equation ... 

The combined gas law is (PiVi/Tj) = (P2V2/T2). It is possible to simplify this equation in this problem by removing all variables not appearing in the table. The simplified combined gas law is (V/Tj) = (V2/T2), which is a form of Charles law. After simplification, we need to isolate the variable we are seeking (the one with the question mark in the table). Isolation of T2 requires manipulating the equation. There are various ways of doing this, all yielding the equation T2 = (T /Vi). We now enter the appropriate values from our table into this equation ... 

In this chapter, you learned about the properties of gases. You learned that you can use the combined gas law, the ideal gas law, or the individual gas laws to calculate certain gas quantities, such as temperature and pressure. You also learned that these equations could also be useful in reaction stoichiometry problems involving gases. You learned the postulates of the Kinetic-Molecular... 

Most gas law experiments use either the combined gas law or the ideal gas equation. Moles of gas are a major factor in many of these experiments. The combined gas law can generate the moles of a gas by adjusting the volume to STP and using Avogadro s relationship of 22.4 L/mol at STE The ideal gas equation gives moles from the relationship n = PV/RT. 

The values of P, T, and n may be used to determine the volume of a gas. If this volume is to be used with Avogadro s law of 22.4 L/mol, the combined gas law must be employed to adjust the volume to STE This equation will use the measured values for P and Talong with the calculated value of V. These values are combined with STE conditions (0°C (273.15 K) and 1.00 atm) to determine the molar volume of a gas. 

Variations in this experiment usually combine the ideal gas equation with the mass of the sample. 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

An equation of this type can be written for N2, CH4 and CO2 and combined with Equation (2.35) and the resulting equation solved to obtain the rates of ebullition and the concentrations of each gas at the sediment surface given the ambient atmospheric concentrations, the rate of methanogensis and the depth of the water. 

If we adopt as the standard state for gaseous components the state of pure perfect gas at P = 1 bar and T = 298.15 K = f% = 1) and neglect for simphcity the fugacity coefficients, equation 5.304 combined with equation 5.297 gives... 

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