a gas is contained in a thick - walled balloon with an initial temperature of 303 k. when the pressure…

Explanation:

Step1: Identify the combined - gas law formula

The combined - gas law is $\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$, where $P_1$ and $P_2$ are initial and final pressures, $V_1$ and $V_2$ are initial and final volumes, and $T_1$ and $T_2$ are initial and final temperatures.

Step2: Rearrange the formula to solve for $T_2$

$T_2=\frac{P_2V_2T_1}{P_1V_1}$

Step3: Substitute the given values

$P_1 = 100.0\ kPa$, $V_1=2.50\ L$, $T_1 = 303\ K$, $P_2 = 90.0\ kPa$, $V_2 = 3.75\ L$. $T_2=\frac{90.0\ kPa\times3.75\ L\times303\ K}{100.0\ kPa\times2.50\ L}$

Step4: Calculate the value of $T_2$

First, calculate the numerator: $90.0\times3.75\times303=90.0\times1136.25 = 102262.5$. Then, calculate the denominator: $100.0\times2.50 = 250$. $T_2=\frac{102262.5}{250}=409.05\ K$

Answer:

$409\ K$