KClO3 decomposes according to the reaction below. How many grams of KClO3 are needed to produce 826ml of O2 at standard temperature and pressure?

2KClO3 → 2KCl + 3O2

To determine the number of grams of KClO3 needed to produce a certain volume of O2 at standard temperature and pressure (STP), we need to follow several steps.

Step 1: Determine the volume of O2 in liters at STP.
STP conditions are defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (1 atm). We have 826 mL of O2, which needs to be converted to liters:
826 mL = 826/1000 = 0.826 L.

Step 2: Use the stoichiometry of the balanced equation to find the molar ratio.
According to the balanced equation, 2 moles of KClO3 produce 3 moles of O2.
So, the molar ratio of KClO3 to O2 is 2:3.

Step 3: Convert the volume of O2 to moles using the ideal gas law.
The ideal gas law equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is temperature in Kelvin.
Given that the pressure is 1 atm, the volume V is 0.826 L, and the temperature T is 273.15 K, we can rearrange the equation to solve for n:
n = PV/RT = (1 atm × 0.826 L) / (0.0821 L·atm/mol·K × 273.15 K) = 0.0301 mol.

Step 4: Use the molar ratio to calculate the moles of KClO3 needed.
Since the molar ratio of KClO3 to O2 is 2:3, we can set up a proportion:
2 moles of KClO3 / 3 moles of O2 = x moles of KClO3 / 0.0301 moles of O2.
Cross-multiplying gives us:
2 × 0.0301 = 3 × x,
0.0602 = 3x,
x = 0.0602/3 ≈ 0.02007 moles of KClO3.

Step 5: Convert moles of KClO3 to grams using molar mass.
The molar mass of KClO3 is calculated by summing the atomic masses of its constituents:
K (39.10 g/mol) + Cl (35.45 g/mol) + 3O (16.00 g/mol) = 122.55 g/mol.
To convert moles of KClO3 to grams, we multiply by the molar mass:
0.02007 moles × 122.55 g/mol ≈ 2.45 grams.

Therefore, approximately 2.45 grams of KClO3 are needed to produce 826 mL of O2 at STP.

Use PV = nRT and solve for n = mols.

Convert mols O2 to mols KClO3 using the coefficients in the balanced equation. then grams KClO3 = mols KClO3 x molar mass KClO3.