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

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

Answer 2

`\boxed {\boxed {\sf 339 \ K }}`

Step-by-step 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}=(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}= (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}= (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.