a gas is stored in a sealed container. if the pressure increases from 750 mm hg to 910 mm hg and the volume…

a gas is stored in a sealed container. if the pressure increases from 750 mm hg to 910 mm hg and the volume decreases from 2.0 l to 1.5 l, what is the initial temperature if the final temperature is 300 k?

a gas is stored in a sealed container. if the pressure increases from 750 mm hg to 910 mm hg and the volume decreases from 2.0 l to 1.5 l, what is the initial temperature if the final temperature is 300 k?

Answer

Explanation:

Step1: Recall the combined - gas law

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. We need to solve for $T_1$. Rearranging the formula gives $T_1=\frac{P_1V_1T_2}{P_2V_2}$.

Step2: Identify the given values

$P_1 = 750\ mmHg$, $V_1=2.0\ L$, $P_2 = 910\ mmHg$, $V_2 = 1.5\ L$, $T_2=300\ K$.

Step3: Substitute the values into the formula

$T_1=\frac{750\times2.0\times300}{910\times1.5}$. First, calculate the numerator: $750\times2.0\times300 = 750\times600=450000$. Then, calculate the denominator: $910\times1.5 = 1365$. Now, $T_1=\frac{450000}{1365}\approx330\ K$.

Answer:

$330\ K$