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What is an ideal gas? Give one reason why a real gas like carbon dioxide deviates from ideal behaviour - Leaving Cert Chemistry - Question a - 2006

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What is an ideal gas? Give one reason why a real gas like carbon dioxide deviates from ideal behaviour. Assuming ideal behaviour, how many moles of carbon dioxide ... show full transcript

Worked Solution & Example Answer:What is an ideal gas? Give one reason why a real gas like carbon dioxide deviates from ideal behaviour - Leaving Cert Chemistry - Question a - 2006

Step 1

What is an ideal gas?

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An ideal gas is a hypothetical gas that perfectly obeys the gas laws, including Boyle's law and the kinetic theory, under all conditions of temperature and pressure. This means that an ideal gas has no intermolecular forces, and the volume of the individual gas molecules is negligible compared to the volume of the container.

Step 2

Give one reason why a real gas like carbon dioxide deviates from ideal behaviour.

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One reason carbon dioxide deviates from ideal behaviour is due to intermolecular forces. Real gases experience attractions between molecules, known as intermolecular forces, which can lead to deviations from the predictions of ideal gas behavior, particularly at high pressures and low temperatures.

Step 3

Assuming ideal behaviour, how many moles of carbon dioxide are present in 720 cm³ of the gas at 10 °C and a pressure of 1 × 10² Pa? Give your answer correct to one significant figure.

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To calculate the number of moles, we use the ideal gas equation:

PV=nRTPV = nRT

Where:

  • P = pressure in pascals = 1imes1021 imes 10^2 Pa
  • V = volume in cubic meters = 720extcm3=0.00072extm3720 ext{ cm}^3 = 0.00072 ext{ m}^3
  • R = ideal gas constant = 8.31extJ/(molK)8.31 ext{ J/(mol K)}
  • T = temperature in kelvins = 10°C+273.15=283.15extK10 °C + 273.15 = 283.15 ext{ K}

Plugging in the values:

n = rac{PV}{RT} = rac{(1 imes 10^2) imes (0.00072)}{(8.31) imes (283.15)}

Calculating this gives:

next(moles)=0.03extmoln ext{ (moles)} = 0.03 ext{ mol}

Thus, the number of moles of carbon dioxide present is 0.03 mol.

Step 4

How many molecules of carbon dioxide are present in this quantity of carbon dioxide?

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To find the number of molecules, we use Avogadro's number, which is approximately 6.022imes10236.022 imes 10^{23} molecules/mol. The calculation is as follows:

extNumberofmolecules=nimesNA=0.03imes6.022imes1023 ext{Number of molecules} = n imes N_A = 0.03 imes 6.022 imes 10^{23}

Calculating this gives:

extNumberofmoleculesext(CO2ext)=1.8imes1022extmolecules ext{Number of molecules} ext{ (CO}_2 ext{)} = 1.8 imes 10^{22} ext{ molecules}

Step 5

What mass of calcium hydroxide is required to react completely with the quantity of carbon dioxide gas given in (iii) above?

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From the balanced chemical equation:

ightarrow ext{CaCO}_3 + ext{H}_2 ext{O} $$ 1 mole of CO₂ reacts with 1 mole of Ca(OH)₂. We found in (iii) that there are 0.03 mol of CO₂, thus: $$ ext{Moles of Ca(OH)}_2 = 0.03 ext{ mol} $$ To find the mass, we use the molar mass of calcium hydroxide, which is approximately 74.09 g/mol: $$ ext{Mass} = ext{moles} imes ext{molar mass} = 0.03 imes 74.09 ext{ g/mol} $$ Calculating this gives: $$ ext{Mass} = 2.22 ext{ g} $$ Therefore, 2.22 g of calcium hydroxide is required.

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