Question

1. choose the best answer. use significant figures.

use the combined gas law to solve for the initial pressure.
$p_1 = ?$
$v_1 = 750$ ml
$t_1 = 0.0 \\ ^\circ c$
$p_2 = 2.00$ atm
$v_2 = 200.0$ ml
$t_2 = 25.0 \\ ^\circ c$
0.48 atm
0.00 atm
0.59 atm

Explanation:

Step1: Convert temps to Kelvin

$T_1 = 0.0 + 273.15 = 273.15\ \text{K}$
$T_2 = 25.0 + 273.15 = 298.15\ \text{K}$

Step2: Rearrange combined gas law

The combined gas law is $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$, solving for $P_1$ gives:
$P_1 = \frac{P_2V_2T_1}{V_1T_2}$

Step3: Substitute values into formula

$P_1 = \frac{2.00\ \text{atm} \times 200.0\ \text{mL} \times 273.15\ \text{K}}{750\ \text{mL} \times 298.15\ \text{K}}$

Step4: Calculate and apply sig figs

First compute the numerator: $2.00 \times 200.0 \times 273.15 = 109260$
Denominator: $750 \times 298.15 = 223612.5$
$P_1 = \frac{109260}{223612.5} \approx 0.489\ \text{atm}$, rounded to 2 significant figures (from 750 mL) gives $0.49\ \text{atm}$. The closest option is 0.48 atm.

Answer:

0.48 atm