Answer:
About 0.53 g of carbon dioxide needs to be added.
Explanation:
Recall the ideal gas law:
[tex]\displaystyle PV = n RT[/tex]
To determine the amount of carbon dioxide we need, we need to solve for n:
[tex]\displaystyle n = \frac{PV}{RT}[/tex]
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:
[tex]\displaystyle 250\text{ mL } \cdot \frac{1 \text{ L}}{1000 \text{ mL}} = 0.25 \text{ L}[/tex]
Temperature:
[tex]\displaystyle \begin{aligned} K & =( ^\circ C) + 273.15 \\ \\ & = (-24) + (273.15) \\ \\ & = 249 \text{ K}\end{aligned}[/tex]
And pressure:
[tex]\displaystyle 95 \text{ kPa} \cdot \frac{1.00 \text{ atm}}{101.3 \text{ kPa}} = 0.94 \text{ atm}[/tex]
Substitute and evaluate:
[tex]\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}[/tex]
Convert moles to grams:
[tex]\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$_2$}[/tex]
In conclusion, about 0.53 g of carbon dioxide needs to be added.
