At elevated temperatures, sodium chlorate decomposes to produce sodium chloride and oxygen gas. A 0.8915-g sample of impure sodium chlorate was heated until the production of oxygen gas ceased. The oxygen gas collected over water occupied 57.2 mL at a temperature of 22°C and a pressure of 734 torr. Calculate the mass percent of NaClO3 in the original sample. (At 22°C the vapor pressure of water is 19.8 torr.)

2NaClO3 ==> 2NaCl + 3O2

Solve for mols O2.
P gas (O2 + H2O) = 734 mm
PH2O = 19.8
PO2 = 734-19.8 = 714.2 mm
Use PV = nRT and solve for n
Convert to mols NaClO3 using the coefficients in the balanced equation.
mols O2 x (2 mols NaClO3/3 mols O2) = ?
Convert mols NaClO3 to grams. g = mols x molar mass.
%NaClO3 = (g NaClO3/mass sample)*100 = ?

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To calculate the mass percent of NaClO3 in the original sample, we need to determine the mass of NaClO3 and the total mass of the sample.

First, let's calculate the moles of oxygen gas (O2) collected over water using the ideal gas law:

PV = nRT

Where:
P = pressure of oxygen gas (converted to atm)
V = volume of oxygen gas (converted to liters)
n = number of moles of oxygen gas
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (converted to Kelvin)

Converting the given values:

P = 734 torr - 19.8 torr (vapor pressure of water) = 714.2 torr
V = 57.2 mL = 0.0572 L
T = 22°C + 273.15 = 295.15 K

Converting pressure to atm:
714.2 torr / 760 torr/atm = 0.94 atm

Now we can calculate the number of moles of oxygen gas:
n = PV / RT
n = (0.94 atm) * (0.0572 L) / (0.0821 L.atm/mol.K * 295.15 K)

Calculate n:
n ≈ 0.00231 mol

Since sodium chlorate (NaClO3) decomposes to produce oxygen gas at a 2:3 molar ratio, the number of moles of NaClO3 is:
(2/3) * n ≈ (2/3) * 0.00231 mol

Calculate moles of NaClO3:
0.00154 mol

Now we need to determine the molecular weight of NaClO3. The atomic masses are: Na = 22.99 g/mol, Cl = 35.45 g/mol, and O = 16.00 g/mol.

Molecular weight of NaClO3:
Na = 22.99 g/mol
Cl = 35.45 g/mol
O = 16.00 g/mol

Molecular weight of NaClO3:
22.99 g/mol + (35.45 g/mol) + (3 * 16.00 g/mol)

Molecular weight of NaClO3:
106.44 g/mol

Finally, we can calculate the mass of NaClO3 in the original sample:
mass of NaClO3 = moles of NaClO3 × molecular weight of NaClO3

mass of NaClO3 ≈ 0.00154 mol × 106.44 g/mol

mass of NaClO3 ≈ 0.164 g

Given that the original sample weighed 0.8915 g, the mass percent of NaClO3 is:
mass percent of NaClO3 = (mass of NaClO3 / mass of sample) × 100

mass percent of NaClO3 = (0.164 g / 0.8915 g) × 100

mass percent of NaClO3 ≈ 18.36%

Therefore, the mass percent of NaClO3 in the original sample is approximately 18.36%.