Question

When the pressure that a gas exerts on a sealed container changes from 767 mm Hg to 800 mm Hg, the temperature changes from 325 K to__[?]___K.

Answer 1

Answer:

$\boxed {\boxed {\sf 339 \ K }}$

Explanation:

The question asks us to find the new temperature given a change in pressure. We will use Gay-Lussac's Law, which states the pressure of a gas is directly proportional to the temperature. The formula is:

$\frac {P_1}{T_1}=\frac{P_2}{T_2}$

The pressure changes from 767 millimeters of mercury (P₁) to 800 millimeters of mercury (P₂).

$\frac {767 \ mm \ Hg }{ T_1}= \frac{800 \ mm \ Hg}{ T_2}$

The temperature is initially 325 K (T₁), but we don't know the final temperature or T₂.

$\frac {767 \ mm \ Hg }{ 325 \ K}= \frac{800 \ mm \ Hg}{ T_2}$

We are solving for the final temperature, so we must isolate the variable T₂. Cross multiply. Multiply the first numerator by the second denominator, then the first denominator by the second numerator.

$767 \ mm \ Hg * T_2 = 325 \ K * 800 \ mm \ Hg$

T₂ is being multiplied by 767 millimeters of mercury. The inverse of multiplication is division. Divide both sides by 767 mm Hg.

$\frac {767 \ mm \ Hg * T_2}{767 \ mm \ Hg} = \frac {325 \ K * 800 \ mm \ Hg }{767 \ mm \ Hg}$

$T_2 = \frac {325 \ K * 800 \ mm \ Hg }{767 \ mm \ Hg}$

The units of millimeters of mercury (mm Hg) cancel.

$T_2= \frac {325 \ K * 800 }{767 }$

$T_2= \frac {260,000 }{767} \ K$

$T_2= 338.983050847 \ K$

The original measurements have 3 significant figures, so our answer must have the same. For the number we found, that is the ones place. The 9 in the tenths place tells us to round the 8 up to a 9.

$T_2 \approx 339 \ K$

The temperature changes from 325 Kelvin to 339 Kelvin.

Answer 2

Answer:

the temperature changes finally to 339k because of the increase in pressure of the gas