Final answer:
To calculate the final pressure in the reaction vessel, we use the ideal gas law. We find that the final pressure of PH₃ produced when 6 moles of H₂ reacts with phosphorus at 298 K in a 5.0 L vessel is 4.0 atm. The correct option is (c)
Step-by-step explanation:
The question pertains to calculating the final pressure in a reaction vessel following a chemical reaction where phosphorus reacts with hydrogen gas. To solve this, we can use the ideal gas law, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in kelvins. Given that 6 moles of H₂ react completely, and 4 moles of PH₃ are produced per the balanced equation P₄(s) + 6H₂(g) → 4PH₃(g), the final pressure can be calculated.
Using the ideal gas law rearranged to P = nRT/V, where n is the number of moles of PH₃ products (4 mol), R is 0.0821 atm·L/mol·K (the ideal gas constant), T is 298 K (the given temperature), and V is 5.0 L (the volume of the vessel), we can solve for the final pressure. Then: P = (4 mol × 0.0821 L·atm/K·mol × 298 K) / 5.0 L, which gives us the final pressure of PH₃ in the vessel.