Question

Question #26795

Answer 1

`T_2=2770"°C"`

Explanation:

Gay-Lussac's Law states that for a constant volume and pressure of gas, `P_1/T_1=P_2/T_2`. Rearranged to solve for `T_2`, this is `T_2=(T_1 times P_2)/P_1`.

Keeping in mind that temperature has to be in Kelvin, `T_1=31"°C"+273=304"K"`

Plugging in the values from the problem,
`T_2=(304"K" times 7450"Torr")/(745"Torr")=3040"K"`

And to convert back to Celsius to answer the question,
`T_2=3040"K"-273=2767"°C"`, and rounding to the appropriate number of significant figures gives `2770"°C"`.

Answer 2

The Celsius temperature required to reach `"7450 torr"` is `"2770"^@"C"`.

Explanation:

This is an example of Gay-Lussac's law , which states that the pressure of a gas is directly proportional to its temperature in Kelvins , as long as the amount and volume is held constant. This means that as the pressure increases, the temperature increases, and vice-versa. The equation to use is:

`P_1/T_1=P_2/T_2`

Given:
`P_="745 torr"`
`T_1="31"^@"C"+273.15="304 K"`
`P_2="7450 torr"`

Unknown: `T_2`

Solution
Rearrange the equation to isolate `T_2`. Substitute the given values into the equation and solve.

`T_2=(P_2T_1)/P_1`

`T_2=(7450color(red)cancel(color(black)("torr"))xx304"K")/(745color(red)cancel(color(black)("torr")))="3040 K"` (rounded to three significant figures)

Convert Kelvin Temperature to Celsius Temperature

To convert the temperature in Kelvins to degrees Celsius, subtract `273.15` from the Kelvin temperature.

`3040"K"-273.15=2770^@"C"`, rounded to three significant figures.