Part A Complete the sentences that explain dynamic equilibrium using the generic reaction A (g) = B (g). Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer.
When the generic reaction A (g) = B (g) reaches dynamic equilibrium, the rate of the forward reaction does not equal the rate of the reverse reaction, and the net concentrations of reactant A and product B would. However, this implies that the concentrations of reactant A and product B are equal at equilibrium. Does not imply be constant not be constant.
Consider the reaction: A (g) 2 B (g). The graph plots the concentrations of A and B as a function of time at a constant temperature.
Part a is the equilibrium constant for this reaction at this temperature? Express your answer to two significant figures.
K= 1.0 M [A]
0.5 M [B]
Time
Part a What is the value of Q when each reactant and product is in its standard state? Match the values in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer.
Standard states are defined as 1 M, or 1 atm 22.414 L. So the value of Qc and Qi when the reactants and products are in their standard states is 22.414 0 298.
Part A Why is an equilibrium constant unit less? When calculating the equilibrium constant, which is the ratio of concentration of the reactants to that of the products, the units of concentrations in the ratio cancel out. When calculating the equilibrium expression, the values of concentration or pressure for a reactant or product are ratios of the concentration or pressure to a reference concentration (exactly 1 M) or a reference pressure (exactly 1 atm). When calculating the equilibrium constant, which is the ratio of pressure of the reactants to that of the products, the units of pressure in the ratio cancel out. The equilibrium constant is the ratio of concentration or pressure of the products to that of the reactants; however, both the pressure and the concentration are unit less.
The Correct Answer and Explanation is
Part A – Dynamic Equilibrium Explanation
Corrected Sentence:
When the generic reaction A (g) ⇌ B (g) reaches dynamic equilibrium, the rate of the forward reaction does equal the rate of the reverse reaction, and the net concentrations of reactant A and product B would be constant. However, this does not imply that the concentrations of reactant A and product B are equal at equilibrium.
Equilibrium Constant Calculation
Given the equilibrium concentrations:
- [A] = 1.0 M
- [B] = 0.5 M
For the reaction:
A (g) ⇌ 2 B (g)
The equilibrium constant expression is: Kc=[B]2[A]=(0.5)21.0=0.251.0=0.25K_c = \frac{[B]^2}{[A]} = \frac{(0.5)^2}{1.0} = \frac{0.25}{1.0} = 0.25
Answer:
K = 0.25
Value of Q in Standard State
Standard states are defined as:
- 1 M for solutions
- 1 atm for gases
- 298 K as standard temperature
- 22.414 L is molar volume at STP (not used directly in Q)
Thus, for the standard state where all concentrations are 1 M: Qc=[B]2[A]=(1)21=1Q_c = \frac{[B]^2}{[A]} = \frac{(1)^2}{1} = 1
Answer: Q = 1
Why the Equilibrium Constant is Unitless – Explanation (Approx. 300 words)
The equilibrium constant (K) is considered unitless due to the way it is defined in thermodynamics and how activities are used in equilibrium expressions.
In chemical reactions, the equilibrium constant is derived from the law of mass action, expressed in terms of the activities of the products and reactants. Activity is a dimensionless quantity that accounts for the effective concentration or pressure of a substance in a reaction. For ideal systems:
- The activity of a solute in solution is its concentration divided by the reference concentration (1 M).
- The activity of a gas is its pressure divided by the reference pressure (1 atm).
So, for a reaction like: aA+bB⇌cC+dDaA + bB ⇌ cC + dD
The equilibrium constant is: K=[C]c[D]d[A]a[B]bK = \frac{[C]^c[D]^d}{[A]^a[B]^b}
However, in thermodynamic terms: K=(aC)c(aD)d(aA)a(aB)bK = \frac{(a_C)^c(a_D)^d}{(a_A)^a(a_B)^b}
where aXa_X is the activity of species X.
Since each activity is a ratio (e.g., [C]/1 M), the units cancel out, making the entire equilibrium constant dimensionless.
Although equilibrium constants can appear to have units when calculated from concentrations or pressures, these are not true units in the thermodynamic sense. Textbooks may include units for clarity, but in rigorous chemical thermodynamics, K is unitless because it’s derived from a ratio of activities.
This ensures consistency with related expressions like the Gibbs free energy change: ΔG∘=−RTlnK\Delta G^\circ = -RT \ln K
Here, the logarithm requires a unitless argument, reinforcing the need for K to be dimensionless.
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