A gaseous mixture of 30 percent (by mole fraction) methane and 70 percent carbon dioxide is heat

A gaseous mixture of 30 percent (by mole fraction) methane...

Key Concepts

Equilibrium Constant Expression

For any reversible reaction at equilibrium, the equilibrium constant (K) quantitatively relates the activities (or effective concentrations) of the products and reactants according to the law of mass action. When one of the phases is a pure solid, its activity is taken as unity; therefore, solids do not appear in the equilibrium constant expression. This simplification is important for correctly formulating the expression that governs the reaction’s balance.

Chemical Equilibrium

Chemical equilibrium describes the state in which a reversible reaction proceeds at equal rates in the forward and reverse directions so that the overall composition of the system becomes steady over time. This concept is vital for predicting the final amounts of reactants and products in a system that does not proceed to complete conversion, as it depends on temperature, pressure, and the intrinsic properties of the reaction.

Reaction Stoichiometry and Extent of Reaction

Reaction stoichiometry involves using the balanced chemical equation to relate the amounts of reactants consumed and products formed. By defining an extent of reaction, one can systematically account for how the molar amounts change as the system progresses toward equilibrium. This method allows the determination of the equilibrium composition by linking the stoichiometric coefficients with the initial amounts and the change due to the reaction.

Partial Pressures and Mole Fractions in Gas Mixtures

In gas-phase reactions at a known total pressure, the partial pressure of each component is typically determined by multiplying its mole fraction by the total pressure. Understanding the relationship between mole fractions and partial pressures is essential for applying the equilibrium constant, which is often expressed in terms of partial pressures (or concentrations) in gaseous systems.

Using the Equilibrium Constant to Determine Composition

By combining the equilibrium constant expression with the stoichiometric and partial pressure relationships, one can set up an equation that relates the extent of reaction to the observed pressures or concentrations. Solving this equation yields the equilibrium composition of the reaction mixture. This approach connects thermodynamic data (such as the equilibrium constant) directly with the observable outcome of a reaction.

Transcript

00:01 Gaseous mixture consisting of methane and carbon dioxide is heated here.

00:14 Now the equilibrium composition by more fraction of the resulting mixture is to be found out.

00:35 So here there are certain assumptions that we have to give.

00:40 First, the equilibrium composition consists of methane, carbon, hydrogen, and co2.

00:53 Second, the constituents of the mixture are ideal gases.

01:01 So these are two assumptions that we have to keep in mind.

01:05 Now as we proceed, we see that.

01:09 The stoichiometric and actual reactions in this phase are s for stoichiometry.

01:16 Ch4, c plus 2h2, therefore vch4 equals to 1, vc is equal to 1 and vh2 equals to 2.

01:38 So in the actual case it is for 8 this actual case, 0 .3 ch4 plus 0 .7 co2 gives you x, okay, i'll just write it in a way, x, x, ch4 plus y, by c plus zh2 plus 0 .7 co2.

02:31 So here all the things, you see, this is the reactant, this is the product, and this is inert.

02:46 So considering this, we are moving forward.

02:49 So we had to find out, so some of the, values that are given are temperature is 1200 kelvin, pressure is 1 atm.

03:04 Now they have carbon balance from this equation above.

03:11 0 .3 equals to x plus y, that is equals to y is equal to 0 .3 minus x.

03:23 Now, the hydrogen balance from the equation is 1 .2 is equal to 4x plus 2 z.

03:36 That gives you z is equal to 0 .6 minus 2x.

03:44 So the total number of moles, which is n total, that is equals to x plus y plus z plus 1 equals to 1 .6 minus 2x.

04:20 Now, the equilibrium constant relation can be expressed as kp equals to nvc h4, c h4, this is the total number of moles upon nc vc, bc upon n c h 4.

04:48 H2 vh2 into p upon in total vch4 minus vc minus vh2.

05:10 I'm putting all the values from the problem stated, that is at 2 or 1 ,200 kelvin, lnkp from the table we get to be 4 .147.

05:28 Therefore, kp is equals to exponent 4 .147, that is equals to 63 .244...

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