# A student adds 5.00 g of dry ice (solid CO_2) to an empty balloon. What will be the volume of the balloon at STP after all the dry ice sublimes (converts to gaseous CO_2)?

May 5, 2016

$V = 2.56 L$

#### Explanation:

Assuming that the $C {O}_{2}$ gas is behaving ideally, therefore, we can use the ideal gas law to find the volume occupied by the gas in a ballon by:

$P V = n R T \implies V = \frac{n R T}{P}$

At STP, the pressure is $P = 1 a t m$ and the temperature is $T = 273 K$.

To find the number of mole of $C {O}_{2}$, we can use the given mass as:

$n = \frac{m}{M M}$, where $M M = 44 \frac{g}{m o l}$ is the molar mass of $C {O}_{2}$.

$\implies n = \frac{5.00 \cancel{g}}{44 \frac{\cancel{g}}{m o l}} = 0.114 m o l$

Therefore, the volume is:
$\implies V = \frac{n R T}{P} = \frac{0.114 \cancel{m o l} \times 0.0821 \frac{L \cdot \cancel{a t m}}{\cancel{K} \cdot \cancel{m o l}} \times 273 \cancel{K}}{1 \cancel{a t m}} = 2.56 L$