find value of x if 36.6 gm BaCl2.XH2O on strong heating loses 5.4 gm moisture?

please tell me

To find the value of x in the compound BaCl₂·xH₂O, we need to analyze the information given about the mass of the hydrated barium chloride and the moisture lost upon heating. Let's break this down step by step.

Understanding the Problem

We start with 36.6 grams of BaCl₂·xH₂O, which is a hydrated form of barium chloride. When we heat this compound, it loses moisture, specifically 5.4 grams of water (H₂O). Our goal is to determine how many water molecules (x) are associated with each formula unit of BaCl₂.

Calculating the Mass of Anhydrous BaCl₂

First, we need to find the mass of the anhydrous BaCl₂ after the moisture has been removed. We can do this by subtracting the mass of the lost water from the initial mass:

• Initial mass of BaCl₂·xH₂O = 36.6 g
• Mass of lost moisture = 5.4 g
• Mass of BaCl₂ after heating = 36.6 g - 5.4 g = 31.2 g

Finding Molar Masses

Next, we need to calculate the molar masses of BaCl₂ and H₂O:

• Barium (Ba) = 137.33 g/mol
• Chlorine (Cl) = 35.45 g/mol (2 Cl atoms = 70.90 g/mol)
• Molar mass of BaCl₂ = 137.33 g/mol + 70.90 g/mol = 208.23 g/mol
• Water (H₂O) = 2(1.01 g/mol) + 16.00 g/mol = 18.02 g/mol

Calculating Moles of BaCl₂

Now, we can find out how many moles of BaCl₂ we have in the 31.2 grams:

Number of moles of BaCl₂ = mass / molar mass = 31.2 g / 208.23 g/mol ≈ 0.150 moles

Relating Moles of Water to Moles of BaCl₂

Since we lost 5.4 grams of water, we can convert this mass into moles as well:

Number of moles of H₂O = mass / molar mass = 5.4 g / 18.02 g/mol ≈ 0.299 moles

Finding the Value of x

In the hydrated compound BaCl₂·xH₂O, the number of moles of water (H₂O) is equal to x times the number of moles of BaCl₂. Therefore, we can set up the following relationship:

x = moles of H₂O / moles of BaCl₂ = 0.299 moles / 0.150 moles ≈ 1.993

Final Calculation

Since x must be a whole number, we round 1.993 to the nearest whole number, which is 2. Thus, the value of x is:

In conclusion, the hydrated barium chloride BaCl₂·2H₂O contains two water molecules for each formula unit of BaCl₂. This process illustrates how stoichiometry and molar mass calculations can help us understand the composition of hydrated compounds.