Consider the reaction below :
P4(s) + 5O2(g) P4O10(s)
How many grams of phosphorus react with 1.195 x 102 L of oxygen (O2) at STP (standard temperature and pressure) to form tetraphosphorus decaoxide?
find moles of O2 first.
Then, use the equation: for every five mole of O2, you need one mole of P4, so figure that out, and convert moles of P4 to grams.
To determine the mass of phosphorus that reacts with 1.195 × 10^2 L of oxygen at STP, we need to use the molar ratio of phosphorus (P4) to oxygen (O2) in the balanced chemical equation.
The balanced equation is:
P4(s) + 5O2(g) → P4O10(s)
From the equation, we can see that the molar ratio of phosphorus to oxygen is 1:5. This means that for every 1 mole of phosphorus, we need 5 moles of oxygen.
First, we need to convert the volume of oxygen gas (1.195 × 10^2 L) to moles using the ideal gas equation (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.
At STP, the pressure is 1 atm, and the temperature is 273.15 K. The ideal gas constant, R, is 0.0821 L·atm/(mol·K).
Using the ideal gas equation:
n = PV / RT
n = (1 atm) × (1.195 × 10^2 L) / (0.0821 L·atm/(mol·K) × 273.15 K)
n ≈ 5.0788 moles of oxygen
Since the molar ratio of phosphorus to oxygen is 1:5, the number of moles of phosphorus is:
moles of phosphorus = 1/5 × moles of oxygen
moles of phosphorus = 1/5 × 5.0788 moles
moles of phosphorus ≈ 1.0158 moles
Finally, to find the mass of phosphorus, we multiply the number of moles by its molar mass. The molar mass of phosphorus (P4) is 4 × atomic mass of phosphorus (P).
The atomic mass of phosphorus (P) is approximately 31. The molar mass of phosphorus (P4) is 4 × 31 = 124 g/mol.
mass of phosphorus = moles of phosphorus × molar mass of phosphorus
mass of phosphorus ≈ 1.0158 moles × 124 g/mol
mass of phosphorus ≈ 125.9932 g
Therefore, approximately 126 grams of phosphorus react with 1.195 × 10^2 L of oxygen to form tetraphosphorus decaoxide.
To find out the number of grams of phosphorus that react with 1.195 x 10^2 L of oxygen at STP to form tetraphosphorus decaoxide, you can use the concept of stoichiometry and the molar ratios from the balanced chemical equation.
Here's how you can solve it step by step:
Step 1: Write down the balanced chemical equation:
P4(s) + 5O2(g) → P4O10(s)
This equation tells us that for every 1 mole of P4 (phosphorus), 5 moles of O2 (oxygen) are required to produce 1 mole of P4O10 (tetraphosphorus decaoxide).
Step 2: Convert the given volume of oxygen to moles at STP.
To do this, we need to use the ideal gas law equation: PV = nRT.
Since we are at STP (standard temperature and pressure), the values for ideal gas law can be simplified.
- The temperature(T) is 273 K
- The pressure(P) is 1 atm
- The gas constant(R) is 0.0821 L·atm/mol·K
Using the equation: n = PV/RT
n = (1.195 x 10^2 L) x (1 atm) / (0.0821 L·atm/mol·K) x (273 K)
Solve for n to find the number of moles of oxygen:
n ≈ 5.96 moles of O2
Step 3: Use the molar ratio from the balanced equation to determine the number of moles of phosphorus.
From the balanced equation, we can see that the ratio of P4 to O2 is 1:5. Therefore, the number of moles of P4 will be 1/5 of the number of moles of O2.
moles of P4 = (5.96 moles of O2) / 5
moles of P4 ≈ 1.192 moles of P4
Step 4: Calculate the mass of phosphorus.
To calculate the mass of phosphorus, we need to use the molar mass of P4, which is 123.89 g/mol.
mass of P4 = moles of P4 x molar mass of P4
mass of P4 = 1.192 moles x 123.89 g/mol
Solve for the mass of P4:
mass of P4 ≈ 148.06 grams
Therefore, approximately 148.06 grams of phosphorus will react with 1.195 x 10^2 L of oxygen at STP to form tetraphosphorus decaoxide (P4O10).