Question

How many grams of CO2 should be placed in a 250 mL container and -24°C to produce a pressure of 95K PA?

Answer 1

Answer:

About 0.53 g of carbon dioxide needs to be added.

Explanation:

Recall the ideal gas law:

$\displaystyle PV = n RT$

To determine the amount of carbon dioxide we need, we need to solve for n:

$\displaystyle n = \frac{PV}{RT}$

Recall that P, V, and T are in atm, L, and K, respectively. R is the universal gas constant.

Convert all values into the correct units:

Volume:

$\displaystyle 250\text{ mL } \cdot \frac{1 \text{ L}}{1000 \text{ mL}} = 0.25 \text{ L}$

Temperature:

$\displaystyle \begin{aligned} K & =( ^\circ C) + 273.15 \\ \\ & = (-24) + (273.15) \\ \\ & = 249 \text{ K}\end{aligned}$

And pressure:

$\displaystyle 95 \text{ kPa} \cdot \frac{1.00 \text{ atm}}{101.3 \text{ kPa}} = 0.94 \text{ atm}$

Substitute and evaluate:

$\displaystyle\begin{aligned} n & = \frac{\left(0.94 \text{ atm}\right)\left(0.25 \text{ L}\right)}{\left(\dfrac{0.08206 \text{ L-atm}}{\text{mol-K}}\right)\left(249\text{ K}\right)} \\ \\ & = 0.012 \text{ mol CO _2 }\end{aligned}$

Convert moles to grams:

$\displaystyle 0.012 \text{ mol CO _2 } \cdot \frac{44.01 \text{ g CO _2 }}{1 \text{ mol CO _2 }} = 0.53 \text{ g CO _2 }$

In conclusion, about 0.53 g of carbon dioxide needs to be added.