# Question 5a3fa

Apr 10, 2017

2000K
(non rounded: 1638K)

#### Explanation:

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

The conditions of STP for gases is 0˚ C and 1 atm

We need to convert our units for the equation written above to be applicable.

${P}_{1}$-- 1 atm
${V}_{1}$-- 0.03 Liters
${T}_{1}$-- 273 Kelvin, 0˚C + 273= Kelvin

${P}_{2}$-- 3 atm: 1 atm = 760 mmHg $\frac{2280 m m H g}{760} = 3 a t m$
${V}_{2}$-- 0.06 Liters
${T}_{2}$-- We will solve for this as a variable

$\frac{.03 \times 1}{273} = \frac{3 \times 0.06}{x}$ Now just finish this through simple algebra to get 1638 K

There is 1 significant digit in the rounded version (since 30 and 60 ml have 1 sig fig), Final Answer: 2000K

Apr 10, 2017

Use the combined gas law for this question.

The final temperature will be$\approx \text{2000 K}$.

#### Explanation:

There are three variables in this question, volume $\left(V\right)$, temperature $\left(T\right)$, and pressure $\left(P\right)$. These variables represent the combined gas law . The equation is:

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

where ${P}_{1}$ is the initial pressure in kilopascals (kPa), ${V}_{1}$ is the initial volume, ${T}_{1}$ is the initial temperature in Kelvins, ${P}_{2}$ is the final pressure in kPa, ${V}_{2}$ is the final volume, and ${T}_{2}$ is the final temperature in Kelvins.

As you can see, we will need to make some conversions of the units for the variables.

STP
STP is currently ${0}^{\circ} \text{C}$, or $\text{273.15 K}$ for gas laws. Pressure is $\text{10^5 Pa}$ or $\text{100 kPa}$. The pressure needs to be converted from $\text{mmHg}$ to $\text{kPa}$.

List what is known/given:
${P}_{1} = \text{100 kPa}$
${V}_{1} = \text{30 mL}$
${T}_{1} = \text{273.15 K}$
P_2=2280color(red)cancel(color(black)("mmHg"))xx(1 "kPa")/(7.50061561303color(red)cancel(color(black)("mmHg")))="303.9750492 kPa"
${V}_{2} = \text{60 mL}$

List what is unknown: ${T}_{2}$

Solution
Rearrange the combined gas law to isolate ${T}_{2}$. Substitute the known values into the equation and solve.

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

T_2=(303.9750492color(red)cancel(color(black)("kPa"))xx60color(red)cancel(color(black)("mL"))xx273.15"K")/(100color(red)cancel(color(black)("kPa"))xx30color(red)cancel(color(black)("mL")))="2000 K"# rounded to one significant figure