There are many oxides of silver with the formula AgxOy. All of them decompose into their elements when heated strongly.
After heating 3.760 g of a silver oxide 3.275 g of silver remained. Determine the empirical formula of AgxOy.
To determine the empirical formula, we first need to find the amount of oxygen that was present in the silver oxide. We can do this by subtracting the mass of silver that remained from the initial mass of the silver oxide:
Mass of oxygen = Initial mass of silver oxide - Mass of silver that remained
Mass of oxygen = 3.760 g - 3.275 g
Mass of oxygen = 0.485 g
Next, we need to find the ratio of silver to oxygen in the compound. We can assume that the ratio is in the form AgxOy, where x and y are integers. To find these integers, we can use the mass of silver and oxygen to calculate the molar ratios:
Molar ratio of Ag to O = Mass of Ag / Atomic mass of Ag : Mass of O / Atomic mass of O
Molar ratio of Ag to O = 3.275 g / 107.87 g/mol : 0.485 g / 16.00 g/mol
Molar ratio of Ag to O = 0.0304 mol Ag : 0.0303 mol O
We want to find the simplest whole number ratio, so we divide both values by the lower one:
Molar ratio of Ag to O = 1.00 mol Ag : 1.00 mol O
This means that there is one atom of silver for every atom of oxygen in the compound. Therefore, the empirical formula is AgO.
To determine the empirical formula of AgxOy, we need to calculate the mole ratios of silver (Ag) and oxygen (O) in the given compound.
Step 1: Calculate the moles of Ag in the given sample.
Molar mass of Ag = 107.87 g/mol
Moles of Ag = Mass of Ag / Molar mass of Ag
= 3.275 g / 107.87 g/mol
≈ 0.030 g (approximately)
Step 2: Calculate the moles of O in the given sample.
We know that the remaining mass after heating is the mass of Ag. Therefore, the mass of O in the given sample is:
Mass of O = Initial mass of Ag - Remaining mass of Ag
= 3.760 g - 3.275 g
= 0.485 g
Molar mass of O = 16.00 g/mol
Moles of O = Mass of O / Molar mass of O
= 0.485 g / 16.00 g/mol
≈ 0.030 g (approximately)
Step 3: Determine the mole ratio of Ag to O.
The mole ratio is the simplest ratio of moles for each element.
Ag:O ≈ 0.030 g : 0.030 g
Ag:O = 1:1
Therefore, the empirical formula of AgxOy is AgO.