Question

a balloon filled with neon gas has a volume of 165ml at a temperature of 17.0°c. if the temperature is changed to ___ °c (at constant pressure) the volume of the balloon will expand to 193ml. (record your answer to the nearest tenth)

Explanation:

Step1: Identify the gas - law formula

At constant pressure, we use Charles's law: $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, where $V$ is volume and $T$ is temperature in Kelvin. First, convert Celsius to Kelvin. $T_1 = 17.0+273.15=290.15$ K.

Step2: Rearrange the formula to solve for $T_2$

We know $V_1 = 165$ mL, $T_1 = 290.15$ K, and $V_2 = 193$ mL. Rearranging Charles's law gives $T_2=\frac{V_2T_1}{V_1}$.

Step3: Substitute the values

$T_2=\frac{193\times290.15}{165}$.
$T_2=\frac{55998.95}{165}\approx339.4$ K.

Step4: Convert back to Celsius

$t_2=T_2 - 273.15$. So $t_2=339.4 - 273.15 = 66.3$ °C.

Answer:

$66.3$