Calculating Nitrogen Conversion to Ammonia at 773K Using the Law of Mass Action

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In summary, the law of mass action is used to calculate the fraction of nitrogen that is converted to ammonia when a mixture of one part nitrogen and three parts hydrogen is heated to 773 Kelvin and the final total pressure is 400 bar. The equilibrium constant K at 773 K is 6.9X10-5 and 1 bar is used as the reference pressure, assuming ideal gas behavior.
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A mixture of one part nitrogen and three parts hydrogen is heated to a temperature of 773 Kelvin. Use the law of mass action to calculate the fraction of nitrogen that is converted (atom to atom) to ammonia if the final total pressure is 400 bar. As alwyas, use 1 bar for the reference pressure, and assume for simplicity that the gases behave ideally. The equilibrium constant K = exp(-dG/RT) at 773 K is 6.9X10-5.

Can someone please give me a hint on how to approach this problem
 
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The best 'approach' is to first right down the "law of mass action'! Exactly what does it say?
 
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Sure! To solve this problem, you will need to use the law of mass action, which states that the rate of a chemical reaction is proportional to the product of the concentrations of the reactants raised to the power of their respective stoichiometric coefficients. In this case, the reaction is N2 + 3H2 ⇌ 2NH3.

To start, we need to determine the initial concentrations of N2 and H2 in the mixture. Since the mixture is made of one part N2 and three parts H2, we can assume that the initial concentration of N2 is 1 mol/L and the initial concentration of H2 is 3 mol/L.

Next, we need to determine the equilibrium constant K for this reaction at 773 K. We are given that K = exp(-dG/RT) = 6.9x10^-5. We can rearrange this equation to solve for dG, which is the change in Gibbs free energy for the reaction. dG = -RTlnK = -(8.314 J/mol*K)(773 K)ln(6.9x10^-5) = 22.2 kJ/mol.

Now, we can use the equilibrium constant expression, K = [NH3]^2/([N2]

^3), to calculate the equilibrium concentration of NH3. Since we are assuming ideal gas behavior, we can use the ideal gas law, PV = nRT, to convert the initial concentrations to partial pressures. We know that the total pressure is 400 bar, so we can set up the following equation: (400 bar) = (2x)^2/[(1x)(3x)^3], where x is the equilibrium concentration of NH3 in mol/L. Solving for x, we get x = 0.013 mol/L.

Finally, we can use the equilibrium concentration of NH3 to calculate the fraction of N2 that has been converted to NH3. Since the initial concentration of N2 was 1 mol/L, the fraction of N2 converted to NH3 is 0.013/1 = 0.013, or 1.3%.

So, at a temperature of 773 K and a total pressure of 400 bar, only 1.3% of the initial concentration of N2 will be converted to NH3 according to the law of mass action.

 

1. What is the Law of Mass Action?

The Law of Mass Action is a principle in chemistry that states the rate of a chemical reaction is proportional to the product of the concentrations of the reactants.

2. How is nitrogen converted to ammonia at 773K?

Nitrogen is converted to ammonia at 773K using the Haber-Bosch process, which involves reacting nitrogen and hydrogen gases in the presence of a catalyst and high temperature and pressure.

3. What is the significance of calculating nitrogen conversion to ammonia at 773K?

Calculating nitrogen conversion to ammonia at 773K is important in understanding the efficiency and conditions of the Haber-Bosch process, which is the primary method for producing ammonia for industrial and agricultural use.

4. What factors affect the conversion of nitrogen to ammonia at 773K?

The conversion of nitrogen to ammonia at 773K is affected by the temperature, pressure, catalyst used, and the concentrations of reactants and products according to the Law of Mass Action.

5. How accurate is the calculation of nitrogen conversion to ammonia at 773K?

The accuracy of the calculation depends on the accuracy of the data and parameters used, such as the rate constants and concentrations of reactants and products. It is important to use reliable and precise experimental data to ensure a more accurate calculation.

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