calculate the lowest whole number ratio of
Moles of Mg/moles of O
mass of empty crucible and lid= 36.560
mass of Mg=0.348
mass of crucible, lid, and product=38.229
To calculate the lowest whole number ratio between the moles of Mg and moles of O, we need to determine the number of moles for each element based on the given masses.
Step 1: Calculate the mass of the crucible and lid (without any content):
mass of empty crucible and lid = 36.560 g
Step 2: Calculate the mass of Mg:
mass of Mg = 0.348 g
Step 3: Calculate the mass of the product:
mass of crucible, lid, and product = 38.229 g
Step 4: Calculate the mass of O (oxygen) by subtracting the mass of the crucible, lid, and Mg from the total mass of the crucible, lid, and product:
mass of O = mass of crucible, lid, and product - mass of empty crucible and lid - mass of Mg
mass of O = 38.229 g - 36.560 g - 0.348 g = 1.321 g
Step 5: Calculate the number of moles for Mg and O using their respective molar masses:
Molar mass of Mg = 24.31 g/mol
Molar mass of O = 16.00 g/mol
moles of Mg = mass of Mg / molar mass of Mg = 0.348 g / 24.31 g/mol
moles of O = mass of O / molar mass of O = 1.321 g / 16.00 g/mol
Step 6: Determine the lowest whole number ratio between the moles of Mg and moles of O by dividing both moles by the smaller value:
moles ratio = moles of Mg / moles of O = (0.348 g / 24.31 g/mol) / (1.321 g / 16.00 g/mol)
Simplify the ratio:
moles ratio = (0.348 g * 16.00 g/mol) / (1.321 g * 24.31 g/mol)
moles ratio = 5.568 g·mol/g / 32.038 g·mol/g
Convert the ratio to the lowest whole number ratio by dividing both values by their greatest common divisor (GCD):
moles ratio = 5.568 / GCD(5.568, 32.038) : 32.038 / GCD(5.568, 32.038)
The GCD of 5.568 and 32.038 is 0.038.
moles ratio ≈ 5.568 / 0.038 : 32.038 / 0.038
moles ratio ≈ 146.526 : 843.632
Step 7: Round the ratio to the lowest whole number values:
moles ratio ≈ 147 : 844
Therefore, the lowest whole number ratio of moles of Mg to moles of O is 147:844.