A hydrate of barium perchlorate, Ba(ClO4)2 • xH2O, contains 35.2% of barium by mass. Find the value of x.
First, we need to determine the formula weight of the hydrate.
Formula weight of Ba(ClO4)2 = 2(Ba) + 2(ClO4) = 2(137.33 g/mol) + 2(99.45 g/mol) = 520.52 g/mol
Next, we can use the given percentage of barium by mass to calculate the mass of barium in one mole of the hydrate.
Mass of Ba in 1 mole of hydrate = 0.352 × formula weight of hydrate
= 0.352 × 520.52 g/mol = 183.45 g/mol
Now, we need to find the mass of water in the hydrate.
Mass of water in 1 mole of hydrate = Formula weight of hydrate − Mass of Ba in 1 mole of hydrate
= 520.52 g/mol − 183.45 g/mol = 337.07 g/mol
Finally, we can use the molar mass of water (18.02 g/mol) to find the value of x.
x = Mass of water in 1 mole of hydrate ÷ Molar mass of water
= 337.07 g/mol ÷ 18.02 g/mol ≈ 18.7
Therefore, the hydrate is Ba(ClO4)2 • 18.7H2O.
To find the value of x in the hydrate of barium perchlorate, we need to use the given information that the hydrate contains 35.2% of barium by mass.
Here's how we can calculate it step by step:
Step 1: Determine the molar mass of Ba(ClO4)2.
The molar mass of Ba(ClO4)2 can be calculated by adding up the molar masses of its individual elements.
Ba (barium) has a molar mass of 137.33 g/mol.
Cl (chlorine) has a molar mass of 35.45 g/mol.
O (oxygen) has a molar mass of 16.00 g/mol.
Therefore, the molar mass of Ba(ClO4)2 is:
2 * (Ba) + (4 * Cl) + (8 * O) = 137.33 * 2 + 35.45 * 4 + 16.00 * 8 = 508.96 g/mol.
Step 2: Determine the mass of barium in Ba(ClO4)2.
Since barium constitutes 35.2% of the hydrate's mass, we can calculate its mass by multiplying the molar mass of Ba(ClO4)2 by the proportion:
mass of barium = 35.2% * mass of Ba(ClO4)2
mass of barium = (35.2/100) * 508.96 g = 179.35 g
Step 3: Determine the molar mass of barium in Ba(ClO4)2.
The atomic mass of barium is 137.33 g/mol.
Let's calculate the number of moles of barium:
moles of barium = mass of barium / molar mass of barium
moles of barium = 179.35 g / 137.33 g/mol = 1.3057 mol
Step 4: Determine the molar mass of water (H2O).
Water (H2O) has a molar mass of 18.02 g/mol.
Step 5: Determine the value of x.
To find x in Ba(ClO4)2 • xH2O, we need to compare the ratio of moles of water to moles of barium. Since the ratio of moles in the compound is 1:1, x is equal to the number of moles of water, which is equal to the number of moles of barium.
Therefore, x = 1.3057 mol.
So, the value of x in the hydrate of barium perchlorate, Ba(ClO4)2 • xH2O is 1.3057.
To find the value of x in the hydrate Ba(ClO4)2 • xH2O, we need to use the information that the hydrate contains 35.2% of barium by mass.
The molar mass of Ba(ClO4)2 is calculated as follows:
Ba (1 atom) = 137.33 g/mol
ClO4 (2 atoms) = 35.453 g/mol (chlorine) + 16.00 g/mol (oxygen) × 4 = 127.36 g/mol
Ba(ClO4)2 = 137.33 g/mol + 127.36 g/mol × 2 = 391.05 g/mol
Now, we can calculate the mass percentage of barium in the hydrate using the molar mass of Ba(ClO4)2:
Mass of Ba = (mass of Ba(ClO4)2 / molar mass of Ba(ClO4)2) × 100%
35.2% = (mass of Ba / 391.05 g/mol) × 100%
Rearranging the equation, we have:
mass of Ba = (35.2% / 100%) × 391.05 g/mol
mass of Ba = 137.77 g/mol
Since the molar mass of Ba(ClO4)2 is the sum of the molar masses of Ba and ClO4, we can conclude that:
mass of Ba = (mass of Ba(ClO4)2 - (molar mass of ClO4 × 2)) / (molar mass of H2O)
137.77 g/mol = (391.05 g/mol - (127.36 g/mol × 2)) / (molar mass of H2O)
Simplifying further:
137.77 g/mol = 136.33 g/mol / (molar mass of H2O)
(molar mass of H2O) = 136.33 g/mol / 137.77 g/mol
Finally, we can determine the value of x by calculating the ratio of the molar mass of water (H2O) to the molar mass of Ba(ClO4)2:
(molar mass of H2O) / (molar mass of Ba(ClO4)2) = x / 2
(x / 2) = 136.33 g/mol / 137.77 g/mol
x = (2 × 136.33 g/mol) / 137.77 g/mol
Calculating the value of x:
x = 272.66 g/mol / 137.77 g/mol
x ≈ 1.980
Therefore, the value of x in the hydrate Ba(ClO4)2 • xH2O is approximately 1.980.