Reaction Quotient With Pressure: Formula and Example

To calculate a reaction quotient using pressure, substitute the current partial pressure of each gaseous reactant and product into the equilibrium-constant expression, raising each pressure to its stoichiometric coefficient. This calculator finds the dimensionless pressure-based quotient, Qp; enter partial pressures in bar and balanced-equation coefficients to see whether the mixture is below, at, or above equilibrium.

Formula

For the reaction mA(g) ⇌ nB(g), the pressure reaction quotient is Qp = (pB/p°)ⁿ / (pA/p°)^m. Here, pA is the current partial pressure of gaseous reactant A, pB is the current partial pressure of gaseous product B, and m and n are their coefficients in the balanced chemical equation. The standard pressure p° is 1 bar, so each ratio is dimensionless.

The calculator uses bar as its pressure unit and assumes the reaction has exactly one gaseous reactant and one gaseous product as written above. Its expression, Qp = (bⁿ)/(a^m), is equivalent to the dimensionless formula because both pressures are entered in bar and p° = 1 bar. For reactions with more species, include every gaseous product in the numerator and every gaseous reactant in the denominator, each raised to its coefficient.

Worked Example

Using the defaults, the reaction is A(g) ⇌ B(g), with pA = 1 bar, pB = 1 bar, and both coefficients equal to 1.

1. Write the expression: Qp = (pB/p°)¹ / (pA/p°)¹.
2. Substitute the entered values and p° = 1 bar: Qp = (1 bar / 1 bar) / (1 bar / 1 bar).
3. Evaluate: Qp = 1 / 1 = 1.000.

The result is dimensionless. It is the quotient for the specified pressures, not automatically the equilibrium constant; whether it represents equilibrium depends on the value of Kp at the same temperature.

How to Calculate Qp for a General Reaction

For a balanced reaction written as aA(g) + bB(g) ⇌ cC(g) + dD(g), use:

Qp = (pC/p°)^c(pD/p°)^d / [(pA/p°)^a(pB/p°)^b].

• Balance the chemical equation first. The coefficients become the exponents.
• Identify the current partial pressure of every gaseous species, not just the total pressure.
• Put products in the numerator and reactants in the denominator.
• Divide each pressure by the standard pressure so the expression is dimensionless, then calculate.

For example, for N₂(g) + 3H₂(g) ⇌ 2NH₃(g), Qp = (pNH₃/p°)² / [(pN₂/p°)(pH₂/p°)³]. If the partial pressures are pNH₃ = 0.20 bar, pN₂ = 0.50 bar, and pH₂ = 0.80 bar, then Qp = (0.20)² / [(0.50)(0.80)³] = 0.04 / 0.256 = 0.15625, or about 0.156. This is a quotient for those conditions; compare it with Kp at the same temperature to infer the direction of net change.

Partial Pressure, Total Pressure, and Units

Partial pressure is the pressure contributed by one gas in a mixture. For an ideal gas mixture, it can be found from its mole fraction y and total pressure P: pi = yiP. If a vessel contains several gases, substituting the total pressure for each species’ partial pressure gives the wrong quotient. A pressure measurement alone is insufficient unless the gas composition is also known or can be calculated.

Pressures can be reported in bar, atmospheres (atm), pascals (Pa), or other units, but use one consistent unit and the same standard pressure in the normalized expression. Since p° = 1 bar, a pressure in atm must be converted to bar or divided by the equivalent standard pressure expressed in atm. In general, the final Qp has no unit. Writing a bare pressure product with units can obscure the standard-state convention and make comparisons misleading.

What Qp Says About Reaction Direction

Compare Qp with Kp, the equilibrium constant expressed using gas pressures, for the same balanced reaction and temperature:

• If Qp < Kp, the mixture has a relative shortage of products compared with equilibrium, so net change proceeds toward products.
• If Qp > Kp, it has a relative excess of products, so net change proceeds toward reactants.
• If Qp = Kp, the mixture is at equilibrium and there is no net change in composition, although forward and reverse reactions continue microscopically.

Qp describes the mixture’s present state; Kp describes the equilibrium condition at a given temperature. Calculating Qp by itself does not establish the direction of change: Kp is also needed. Changing pressure can alter the partial pressures and therefore Qp, but it does not by itself change Kp at fixed temperature. Temperature changes can change Kp.

Common Mistakes and Limits

• Using total pressure for every gas: use each species’ partial pressure. For an ideal mixture, calculate it from mole fraction times total pressure.
• Using coefficients as multipliers: coefficients are exponents in the quotient, not factors multiplied by pressure.
• Reversing the ratio: products go on top; reactants go below. Reversing the written equation also inverts Qp.
• Including pure solids or liquids: their activities are treated as 1 in the usual equilibrium expression, so they are omitted. A dissolved species is not a pure liquid and is generally included using its activity or an appropriate concentration expression.
• Rounding too early: retain unrounded pressures and intermediate results, then round the final quotient to a sensible number of significant figures.

The simple pressure expression is most directly applicable to ideal gases. For non-ideal gases, rigorous thermodynamic expressions use fugacities, which account for deviations from ideal behavior. Also, Qp depends on the exact reaction as written: multiplying every equation coefficient by a factor raises the corresponding quotient to that factor. A quoted quotient is meaningful only alongside its reaction equation, pressure convention, and temperature context.

Frequently Asked Questions

How do I calculate Qp from partial pressures?
Write the balanced equation, put product partial pressures over reactant partial pressures, raise each to its coefficient, and normalize pressures by the standard pressure. For the common convention p° = 1 bar, pressures entered in bar can be used directly in the numerical ratios.

Can I use total pressure to calculate the reaction quotient?
Not by itself when multiple gases are present. You need each gas’s partial pressure, which for an ideal mixture is its mole fraction multiplied by the total pressure.

Does Qp have units?
No, when written with pressure divided by the standard pressure, Qp is dimensionless. A calculation that leaves units in the result may have omitted the standard-state normalization.

What is the difference between Qp and Kp?
Qp uses the current partial pressures and can change as the mixture changes. Kp is the equilibrium value at a specified temperature; comparing the two indicates the direction of net reaction.

Do pure solids appear in Qp?
No. Pure solids and pure liquids are omitted from the usual equilibrium expression because their activities are taken as 1. Gaseous species are included, as are relevant dissolved species in the appropriate form.

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in a | Reactant A partial pressure | bar | 1 | 0
in b | Product B partial pressure | bar | 1 | 0
in m | Reactant A coefficient | - | 1 | 0
in n | Product B coefficient | - | 1 | 0
out q | Pressure reaction quotient Qp | - | (b^n)/(a^m) | 3