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The composition of a carbon dioxide (CO₂) molecule is one atom of ¹²C and two atoms of ¹⁶O - AQA - A-Level Physics - Question 10 - 2017 - Paper 2

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The composition of a carbon dioxide (CO₂) molecule is one atom of ¹²C and two atoms of ¹⁶O. What is the number of molecules of CO₂ in 2.2 kg of the gas?

Worked Solution & Example Answer:The composition of a carbon dioxide (CO₂) molecule is one atom of ¹²C and two atoms of ¹⁶O - AQA - A-Level Physics - Question 10 - 2017 - Paper 2

Step 1

Calculate the molar mass of CO₂

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Answer

The molar mass of CO₂ can be calculated as follows:

  • Molar mass of ¹²C: 12 g/mol
  • Molar mass of ¹⁶O: 16 g/mol

Since there is one carbon and two oxygen atoms in CO₂:

extMolarmassofCO2=12+(2imes16)=12+32=44extg/mol ext{Molar mass of CO₂} = 12 + (2 imes 16) = 12 + 32 = 44 ext{ g/mol}

Step 2

Calculate the number of moles in 2.2 kg of CO₂

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Answer

Given that 2.2 kg of CO₂ is equal to 2200 g:

extNumberofmoles=mass (g)molar mass (g/mol)=2200g44g/mol=50 moles ext{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{2200 g}{44 g/mol} = 50 \text{ moles}

Step 3

Calculate the number of molecules in 50 moles of CO₂

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Answer

Using Avogadro's number, which is approximately (6.022 \times 10^{23}) molecules per mole:

Number of molecules=Number of moles×Avogadro’s number\text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number}

So,

Number of molecules=50×6.022×10233.011×1025 molecules\text{Number of molecules} = 50 \times 6.022 \times 10^{23} \approx 3.011 \times 10^{25} \text{ molecules}

Step 4

Identify the correct answer from the options

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Answer

The closest answer to the calculated number of molecules (approximately (3.011 \times 10^{25})) is option C: 3.0×10253.0 \times 10^{25}.

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