Question

During the course of World War I, \(1.1 \times 10^{8} \mathrm{~kg}\) of poison gas was fired on Allied soldiers by German troops. If the gas is assumed to be phosgene \(\left(\mathrm{COC} 1_{2}\right)\), how many molecules of gas does this correspond to?

Short answer

Approximately \(6.69 \times 10^{32}\) molecules of phosgene gas were fired on Allied soldiers by German troops during World War I.

Step-by-step solution

Calculate the molar mass of phosgene

To calculate the molar mass of phosgene (COCl₂), we need to find the molar mass of each atom in the molecule and then add them up. Molar mass of Carbon (C) = 12.01 g/mol Molar mass of Oxygen (O) = 16.00 g/mol Molar mass of Chlorine (Cl) = 35.45 g/mol Now let's add them up for the whole molecule: Molar mass of COCl₂ = 12.01 + 16.00 + 2 × 35.45 = 98.91 g/mol.

Convert mass of phosgene into moles

Now, we need to convert the mass of phosgene (1.1 x 10^8 kg) into moles. To do this, we can use the formula: moles = mass / molar mass First, let's convert the mass of phosgene into grams as the molar mass is in grams. Mass of phosgene = 1.1 x 10^8 kg × 1000 g/kg = 1.1 x 10^11 g Now, we can calculate the moles of phosgene: moles = (1.1 x 10^11 g) / (98.91 g/mol) ≈ 1.1117 x 10^9 mol

Calculate the number of molecules of phosgene

To find the number of molecules, we will use Avogadro's number (6.022 × 10^23 molecules/mol). We can calculate the number of molecules using the formula: Number of molecules = moles × Avogadro's number Number of molecules = (1.1117 x 10^9 mol) × (6.022 x 10^23 molecules/mol) ≈ 6.69 × 10^32 molecules Therefore, 1.1 × 10^8 kg of phosgene gas corresponds to approximately \(6.69 \times 10^{32}\) molecules.

Key concepts

Understanding Molar Mass

Molar mass is a fundamental concept in chemistry that represents the mass of a given substance (chemical element or compound) divided by the amount of substance. It's usually expressed in grams per mole (g/mol).

For phosgene (COCl₂), you need to know the molar mass of each element that makes up the compound to calculate the total molar mass.

• The molar mass of Carbon (C) is 12.01 g/mol
• The molar mass of Oxygen (O) is 16.00 g/mol
• The molar mass of Chlorine (Cl) is 35.45 g/mol

To find the molar mass of the entire phosgene molecule, simply add the masses of all the atoms involved: \[ Molar \ mass \ of \ COCl₂ = 12.01 \text{ g/mol} + 16.00 \text{ g/mol} + 2 \times 35.45 \text{ g/mol} = 98.91 \text{ g/mol} \] This step gives us the molar mass of phosgene, a crucial number for finding out how many moles we have in a given mass of the substance.

Moles Conversion

Converting mass to moles is a common task in chemistry, and it's vital for working with chemical equations and reactions. To perform this conversion, you can use the equation: \[ \text{moles} = \frac{\text{mass of substance (in grams)}}{\text{molar mass of substance (in g/mol)}} \]

In our scenario, the mass of phosgene is given in kilograms, so the first step is converting this mass to grams (since molar mass is often in g/mol). This is done by multiplying by 1000 (since 1 kg = 1000 g): \[ 1.1 \times 10^8 \text{ kg} \times 1000 = 1.1 \times 10^{11} \text{ g} \]

Next, we use the molar mass determined earlier (98.91 g/mol) to find out how many moles there are: \[ \text{moles of phosgene} = \frac{1.1 \times 10^{11} \text{ g}}{98.91 \text{ g/mol}} \approx 1.1117 \times 10^9 \text{ mol} \]

This tells us the quantity of moles in the phosgene mass used during World War I.

Avogadro's Number and Molecules

Avogadro's number is a constant used in chemistry to quantify the number of particles, typically atoms or molecules, within one mole of a substance. It is defined as 6.022 × 10^23 particles per mole.

To figure out how many molecules of phosgene gas there are in a given number of moles, multiply the number of moles by Avogadro's number: \[ \text{Number of molecules} = \text{moles} \times \text{Avogadro's number} \]In this case, the calculation is: \[ 1.1117 \times 10^9 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 6.69 \times 10^{32} \text{ molecules} \]

This step shows the sheer quantity of phosgene molecules used, translating the abstract mole concept into something more tangible by conveying the actual number of molecules present.