how do you calculate the empirical formula of the barium hydroxide hydrate if a sample consists of 3.70 grams of barium hydroxide and 2.64 gras of water???
To calculate the empirical formula of the barium hydroxide hydrate, you need to determine the mole ratio between the elements present in the compound. Here's how you can do it:
Step 1: Convert the given masses of barium hydroxide (Ba(OH)2) and water (H2O) into moles. To do this, divide the given mass by the molar mass of each substance.
The molar mass of Ba(OH)2 can be calculated as follows:
Ba: 1 atom * molar mass of Ba
O: 2 atoms * molar mass of O
H: 2 atoms * molar mass of H
The molar mass of H2O can be determined as:
H: 2 atoms * molar mass of H
O: 1 atom * molar mass of O
Step 2: Find the molar ratio between barium hydroxide and water by dividing the number of moles of each substance by the smallest number of moles obtained in Step 1.
Step 3: Convert the obtained ratios into whole numbers by multiplying them by a common factor that makes the ratio integers.
Step 4: Determine the empirical formula by writing the elements and their subscripts according to the whole number ratios obtained in Step 3.
Following these steps, let's calculate the empirical formula of the barium hydroxide hydrate with 3.70 grams of Ba(OH)2 and 2.64 grams of H2O:
Step 1: Calculate the moles.
Molar mass of Ba(OH)2:
Ba: 1 atom * 137.33 g/mol = 137.33 g/mol
O: 2 atoms * 16.00 g/mol = 32.00 g/mol
H: 2 atoms * 1.01 g/mol = 2.02 g/mol
Molar mass of H2O:
H: 2 atoms * 1.01 g/mol = 2.02 g/mol
O: 1 atom * 16.00 g/mol = 16.00 g/mol
Moles of Ba(OH)2:
3.70 g / (137.33 g/mol + 32.00 g/mol + 2.02 g/mol) = 0.0202 mol
Moles of H2O:
2.64 g / (2.02 g/mol + 16.00 g/mol) = 0.140 mol
Step 2: Find the molar ratio.
Molar ratio of Ba(OH)2 to H2O:
0.0202 mol / 0.0202 mol = 1:1
0.140 mol / 0.0202 mol ≈ 6.93:1 (approximately 7:1)
Step 3: Convert the ratio to whole numbers.
Multiply both ratios by a common factor to obtain whole numbers:
1 * 7 ≈ 7
7 * 1 ≈ 7
Step 4: Based on the whole number ratios, the empirical formula is Ba(OH)2 ⋅ 7H2O.