Question 26795

Apr 16, 2017

${T}_{2} = 2770 \text{°C}$

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 ${T}_{2} = \frac{{T}_{1} \times {P}_{2}}{P} _ 1$.

Keeping in mind that temperature has to be in Kelvin, ${T}_{1} = 31 \text{°C"+273=304"K}$

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,
${T}_{2} = 3040 \text{K"-273=2767"°C}$, and rounding to the appropriate number of significant figures gives $2770 \text{°C}$.

Apr 16, 2017

The Celsius temperature required to reach $\text{7450 torr}$ is $\text{2770"^@"C}$.

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:
${P}_{=} \text{745 torr}$
${T}_{1} = \text{31"^@"C"+273.15="304 K}$
${P}_{2} = \text{7450 torr}$

Unknown: ${T}_{2}$

Solution
Rearrange the equation to isolate ${T}_{2}$. Substitute the given values into the equation and solve.

${T}_{2} = \frac{{P}_{2} {T}_{1}}{P} _ 1$

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.

$3040 \text{K"-273.15=2770^@"C}$, rounded to three significant figures.