A 5.0L reaction vessel contain hydrogen at a partial pressure of 0.588 atm and oxygen gas at a partial pressure of 0.302 atm .The limiting reactant is

To determine the limiting reactant in the reaction between hydrogen and oxygen, we first need to understand the balanced chemical equation for the reaction that produces water:

Balanced Chemical Equation

The reaction can be represented as:

2 H₂(g) + O₂(g) → 2 H₂O(g)

Identifying Moles of Reactants

Next, we need to calculate the number of moles of each reactant present in the reaction vessel. We can use the ideal gas law, which states:

PV = nRT

Where:

• P = pressure (in atm)
• V = volume (in liters)
• n = number of moles
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature (in Kelvin)

Assuming the reaction occurs at standard temperature (298 K), we can calculate the moles of hydrogen and oxygen.

Calculating Moles of Hydrogen

For hydrogen:

P_H₂ = 0.588 atm

V = 5.0 L

n_H₂ = (P_H₂ × V) / (R × T)

Substituting the values:

n_H₂ = (0.588 atm × 5.0 L) / (0.0821 L·atm/(K·mol) × 298 K)

Calculating this gives:

n_H₂ ≈ 0.12 moles

Calculating Moles of Oxygen

For oxygen:

P_O₂ = 0.302 atm

n_O₂ = (P_O₂ × V) / (R × T)

Substituting the values:

n_O₂ = (0.302 atm × 5.0 L) / (0.0821 L·atm/(K·mol) × 298 K)

Calculating this gives:

n_O₂ ≈ 0.06 moles

Determining the Limiting Reactant

Now that we have the moles of each reactant, we can determine which one is the limiting reactant. According to the balanced equation, 2 moles of hydrogen react with 1 mole of oxygen. This means:

• For every 2 moles of H₂, 1 mole of O₂ is required.

We can set up a ratio to see how much oxygen is needed for the available hydrogen:

Required O₂ for 0.12 moles of H₂ = 0.12 moles H₂ × (1 mole O₂ / 2 moles H₂) = 0.06 moles O₂

Since we have exactly 0.06 moles of O₂ available, it will be completely consumed when reacting with the available hydrogen. Therefore, hydrogen is in excess, and oxygen is the limiting reactant.

Final Answer

The limiting reactant in this reaction is oxygen (O₂).