Question

What is the volume of 8.7 * 10 ^ 23 molecules of chlorine gas (Cl 2 ) ?

Answer 1

To find the volume of 8.7 × 1023 molecules of Cl2, convert the number of molecules to moles using Avogadro's number, then multiply by the molar volume of a gas at STP.

Step-by-step explanation:

To calculate the volume of 8.7 × 1023 molecules of chlorine gas (Cl2), we need to use Avogadro's number and the molar volume concept. One mole of a substance contains 6.022 × 1023 molecules, known as Avogadro's number. Therefore, we can determine the moles of Cl2 by dividing the given number of molecules by Avogadro's number:

Number of moles of Cl2 = (8.7 × 1023 molecules) / (6.02 × 1023 molecules/mol)

At standard temperature and pressure (STP), one mole of any gas occupies 22.4 liters. Thus, we can find the volume of chlorine gas by multiplying the moles of Cl2 by 22.4 L/mol:

Volume of Cl2 = Number of moles of Cl2 × 22.4 L/mol

Using this two-step conversion, we can solve for the volume without explicitly calculating the exact number of moles.

Answer 2

32.3 dm³

Step-by-step explanation:

Data given:

no. of molecules of Cl₂ = 8.7 x 10²³

Volume of chlorine gas (Cl₂) = ?

Solution:

First we have to find number of moles

For this formula used

no. of moles = no. of molecules / Avogadros number

no. of moles = 8.7 x 10²³ / 6.022 x 10²³

no. of moles = 1.44 moles

Now we have to find volume of the gas

for this formula used

no. of moles = volume of gas / molar volume

molar volume = 22.4 dm³/mol

Put values in above equation

1.44 moles = volume of Cl₂ gas / 22.4 dm³/mol

rearrange the above equation

volume of Cl₂ gas = 1.44 moles x 22.4 dm³/mol

volume of Cl₂ gas = 32.3 dm³