Question

Jude has a 30.00 L cylinder full of acetylene gas that he will use for welding in his workshop. If the pressure of the cylinder is 1720 kPa and the workshop is at 20.0 °C, then how many moles of acetylene are in the tank? (Show work)

Answer 1

About 21.2 moles.

Step-by-step explanation:

Recall the ideal gas law:

`\displaystyle PV = nRT`

Where P is the pressure of the gas; V is its volume; n is the number of moles of gas; R is the universal gas constant; and T is the absolute temperature.

Rearrange to solve for n:

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

Because R has units of L-atm/mol-K, convert the pressure to atm:

`\displaystyle 1720 \text{ kPa} \cdot \frac{1\text{ atm}}{101.3\text{ kPa}} = 17.0\text{ atm}`

And convert from Celsius to kelvins:

`\displaystyle \begin{aligned}T _ k & = T_C + 273.15 \\ \\ & = (20.0) + 273.15 \\ \\ & = 293.2\text{ K} \end{aligned}`

Hence substitute and evaluate:

`\displaystyle \begin{aligned} n & = (PV)/(RT) \\ \\ & = \frac{\left(17.0\text{ atm})(30.00\text{ L})}{\left(\frac{0.08206\text{ L-atm}}{\text{mol-K}}\right)(293.2\text{ K})} \\ \\ & = 21.2\text{ mol } \end{aligned}`

In conclusion, there are about 21.2 moles of acetylene in the tank.