Question

How many moles of argon are there in a 22.4 L sample of gas at 101.3 kPa and 0 C?

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Answer 1

0.999 moles of argon (3 s.f.)

Step-by-step explanation:

To determine the number of moles of argon in a gas sample, we can use the ideal gas law equation:

Ideal Gas Law

`\boxed{PV=nRT}`

where:

• P is the pressure measured in kilopascals (kPa).
• V is the volume measured in liters (L).
• n is the number of moles.
• R is the ideal gas constant (8.31446261815324 kPa L mol⁻¹ K⁻¹).
• T is the temperature measured in kelvin (K).

Since we are finding "n", rearrange the equation for n:

`\implies n=(PV)/(RT)`

As the temperature has to be measured in kelvin, convert the temperature from Celsius to kelvin by adding 273.15:

`\implies \sf 0^(\circ)=0+273.15\;K=273.15\;K`

Therefore, the values to substitute into the equation are:

• P = 101.3 kPa
• V = 22.4 L
• R = 8.31446261815324 L kPa mol⁻¹ K⁻¹
• T = 273.15 K

Substitute the values into the formula and solve for n:

`\implies n=\sf (101.3\;kPa \cdot 22.4\;L)/(8.314 462...L\;kPa\;mol^(-1)\;K^(-1) \cdot 273.15\;K)`

`\implies n=\sf (101.3\cdot 22.4)/(8.314 462...\;mol^(-1)\cdot 273.15)`

`\implies n=\sf (2269.12\;mol)/(2271.09546...)`

`\implies n=\sf 0.99913017...\;mol`

`\implies n=\sf 0.999\;mol\;(3\;s.f.)`

Therefore, there are 0.999 moles of argon (to three significant figures) in a 22.4 L sample of gas at 101.3 kPa and 0°C.