. What volume of hydrogen gas, at 273 K and 1 atm, pressure will be consumed in obtaining 21.6 g of elemental boron (atomic mass = 10.8) from the reducti on of boron trichloride by hydrogen?

To determine the volume of hydrogen gas consumed in the reduction of boron trichloride (BCl3) to obtain elemental boron (B), we first need to understand the chemical reaction involved. The balanced equation for the reduction of boron trichloride by hydrogen is as follows:

Chemical Reaction

The reaction can be represented as:

2 BCl3 + 3 H2 → 2 B + 6 HCl

This equation tells us that 3 moles of hydrogen gas react with 2 moles of boron trichloride to produce 2 moles of elemental boron and 6 moles of hydrogen chloride.

Calculating Moles of Boron

Next, we need to calculate how many moles of boron correspond to 21.6 grams. The atomic mass of boron is given as 10.8 g/mol. Using the formula:

Number of moles = mass (g) / molar mass (g/mol)

we can find the moles of boron:

Number of moles of B = 21.6 g / 10.8 g/mol = 2 moles

Relating Moles of Boron to Moles of Hydrogen

From the balanced equation, we see that 2 moles of boron are produced from 3 moles of hydrogen. Therefore, to find the moles of hydrogen needed for 2 moles of boron, we can set up a proportion:

For 2 moles of B, we need 3 moles of H2.

Thus, the moles of hydrogen required = (3 moles H2 / 2 moles B) × 2 moles B = 3 moles H2.

Calculating Volume of Hydrogen Gas

Now that we know we need 3 moles of hydrogen gas, we can calculate the volume at standard temperature and pressure (STP), which is defined as 273 K and 1 atm. At STP, 1 mole of an ideal gas occupies 22.4 liters. Therefore, the volume of hydrogen gas can be calculated as follows:

Volume = moles × volume per mole

Volume of H2 = 3 moles × 22.4 L/mole = 67.2 liters.

Final Answer

In summary, the volume of hydrogen gas consumed in obtaining 21.6 g of elemental boron from the reduction of boron trichloride is 67.2 liters at 273 K and 1 atm pressure.