How many grams of phosphorus react with 31.3 L of O2 at STP to form tetraphosphorus decaoxide?
P4(s) + 5 O2(g) -> P4O10(s)
moles O2=31.2/22.4 moles
so you need 1/5 that number moles of P4.
To determine the number of grams of phosphorus that react with 31.3 L of O2 at STP to form tetraphosphorus decaoxide, we can use the ideal gas law to find the number of moles of O2, then use the stoichiometry of the balanced equation to calculate the number of moles of phosphorus, and finally convert moles to grams.
1. Calculate the number of moles of O2:
Using the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature (STP: 0 degrees Celsius or 273.15 Kelvin).
At STP, the pressure is 1 atm, and the temperature is 273.15 K.
Using the given volume (31.3 L) and these values:
PV = nRT
(1 atm) * (31.3 L) = n * (0.0821 L atm/mol K) * (273.15 K)
n = (1 atm * 31.3 L) / (0.0821 L atm/mol K * 273.15 K)
n ≈ 1.21 mol
2. Use stoichiometry to find the number of moles of phosphorus:
From the balanced equation, we can see that there is a 1:1 mole ratio between P4 and P4O10.
Therefore, 1.21 mol of P4O10 will react with 1.21 mol of P4.
3. Convert moles to grams:
The molar mass of P4 is approximately 123.9 g/mol.
To find the mass of phosphorus, we can use the equation:
mass = moles * molar mass
mass = 1.21 mol * 123.9 g/mol
mass ≈ 149.72 g
Therefore, approximately 149.72 grams of phosphorus will react with 31.3 L of O2 at STP to form tetraphosphorus decaoxide.
To find the number of grams of phosphorus that react with 31.3 L of O2 at STP (Standard Temperature and Pressure), we need to use the ideal gas law and the stoichiometry of the balanced chemical equation.
Step 1: Convert the volume of O2 from liters to moles.
At STP, 1 mole of any ideal gas occupies 22.4 liters. Therefore, we can calculate the number of moles of O2 as follows:
31.3 L O2 * (1 mole O2 / 22.4 L O2) = 1.398 moles O2
Step 2: Use stoichiometry to determine the mole ratio between O2 and P4.
According to the balanced chemical equation, 1 mole of P4 reacts with 5 moles of O2. Therefore, we can write the following ratio:
5 moles O2 / 1 mole P4
Step 3: Calculate the number of moles of P4.
To determine the moles of P4, we can multiply the moles of O2 by the mole ratio from step 2:
1.398 moles O2 * (1 mole P4 / 5 moles O2) = 0.2796 moles P4
Step 4: Convert moles of P4 to grams.
The molar mass of P4 is 123.88 g/mol. We can calculate the mass of P4 by multiplying the number of moles by the molar mass:
0.2796 moles P4 * (123.88 g P4 / 1 mole P4) ≈ 34.64 g P4
Therefore, approximately 34.64 grams of phosphorus will react with 31.3 L of O2 at STP to form tetraphosphorus decaoxide.