Question

1. choose the best answer. use significant figures.

use the combined gas law to solve for the final celsius temperature.
$p_1 = 600.0 \text{ mmhg}$
$v_1 = 2.50 \text{ l}$
$t_1 = 22.0 \\ ^\circ\text{c}$
$p_2 = 760 \text{ mmhg}$
$v_2 = 1.80 \text{ l}$
$t_2 = ?$
-3 $^\circ\text{c}$
50 $^\circ\text{c}$
269 $^\circ\text{c}$

Explanation:

Step1: Convert T₁ to Kelvin

$T_1 = 22.0 + 273.15 = 295.15\ \text{K}$

Step2: Rearrange combined gas law

The combined gas law is $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$, rearranged to:
$T_2 = \frac{P_2V_2T_1}{P_1V_1}$

Step3: Substitute values into formula

$T_2 = \frac{760\ \text{mmHg} \times 1.80\ \text{L} \times 295.15\ \text{K}}{600.0\ \text{mmHg} \times 2.50\ \text{L}}$

Step4: Calculate T₂ in Kelvin

$T_2 = \frac{760 \times 1.80 \times 295.15}{600.0 \times 2.50} \approx 270.2\ \text{K}$

Step5: Convert T₂ to Celsius

$T_2 = 270.2 - 273.15 \approx -3.0\ ^\circ\text{C}$

Step6: Apply significant figures

Round to 1 significant figure: $T_2 \approx -3\ ^\circ\text{C}$

Answer:

-3 °C