What mass of potassium nitrate would you have to heat in order to produce 1.00dm of oxygen at rtp?
Write the equation and balance it. What is rtp?
24 -23-09
To determine the mass of potassium nitrate needed to produce 1.00 dm³ of oxygen at RTP (room temperature and pressure), we need to use the balanced chemical equation for the decomposition of potassium nitrate (KNO₃):
2 KNO₃(s) → 2 KNO₂(s) + O₂(g)
According to the equation, for every 2 moles of KNO₃ decomposed, we obtain 1 mole of O₂ gas.
To find the mass of KNO₃, we can follow these steps:
Step 1: Calculate the volume of oxygen in moles
Using the ideal gas law, PV = nRT, we can rearrange the equation to find the number of moles:
n = PV / RT
Since we are given the volume of oxygen (1.00 dm³) at RTP, which is 1.00 × 10³ cm³, we convert it to liters:
V = 1.00 × 10³ cm³ = 1.00 × 10³ ml = 1.00 L
The molar gas constant, R, is 0.0821 L·atm/(mol·K), and the temperature, T, is 298 K (RTP). Assuming the pressure is 1 atm, we can substitute these values into the equation:
n = (1.00 L × 1 atm) / (0.0821 L·atm/(mol·K) × 298 K)
n = 0.0414 mol
Step 2: Determine the moles of KNO₃ needed
Since the balanced equation shows that 2 moles of KNO₃ produce 1 mole of O₂, we can set up a ratio:
2 mol KNO₃ / 1 mol O₂
Therefore, the moles of KNO₃ needed will be twice the moles of O₂:
n(KNO₃) = 2 × 0.0414 mol
n(KNO₃) = 0.0828 mol
Step 3: Calculate the mass of KNO₃
Finally, we can find the molar mass of KNO₃, which is the sum of the atomic masses of its constituent elements:
Molar mass of KNO₃ = (1 × atomic mass of K) + (1 × atomic mass of N) + (3 × atomic mass of O)
Molar mass of KNO₃ = (1 × 39.10 g/mol) + (1 × 14.01 g/mol) + (3 × 16.00 g/mol)
Molar mass of KNO₃ = 101.11 g/mol
The mass of KNO₃ required can be found by multiplying the moles of KNO₃ by its molar mass:
Mass of KNO₃ = n(KNO₃) × Molar mass of KNO₃
Mass of KNO₃ = 0.0828 mol × 101.11 g/mol
Mass of KNO₃ = 8.37 g
Therefore, you would have to heat approximately 8.37 grams of potassium nitrate (KNO₃) to produce 1.00 dm³ of oxygen at RTP.