Question

A canister of acetylene has a volume of 62 L. The temperature of the acetylene is 205 K and the pressure is 740

torr. Determine the amount (moles) of gas in the canister.

Answer 1

3.59 mol (3 s.f.)

Step-by-step explanation:

To determine the number of moles of gas in the canister, we can use the Ideal Gas Law.

Ideal Gas Law

`\boxed{PV=nRT}`

where:

• P is the pressure measured in atmosphere (atm).
• V is the volume measured in liters (L).
• n is the number of moles.
• R is the ideal gas constant (0.082057366080960 atm L mol⁻¹ K⁻¹).
• T is the temperature measured in kelvin (K).

As the given pressure is in torr, we need to convert it to atmospheres (atm). As 1 atm = 760 torr, to convert torr to atm, divide the pressure value by 760:

`\implies \sf 740\;torr=(740)/(760)\;atm=0.9736842105...\;atm`

Therefore, the values to substitute into the equation are:

• P = 0.9736842105 atm
• V = 62 L
• R = 0.082057366080960 atm L mol⁻¹ K⁻¹
• T = 205 K

As we want to find the number of moles, rearrange the equation to isolate n:

`n=(PV)/(RT)`

Substitute the values into the equation and solve for n:

`\implies n=(0.9736842105... \cdot 62)/(0.08205736... \cdot 205)`

`\implies n=(60.3684210...)/(16.821760046...)`

`\implies n=3.58871015193...`

`\implies n=3.59\; \sf mol\;(3\;s.f.)`

Therefore, the number of moles of gas in the canister is 3.59 moles (rounded to three significant figures).