Question #5a3fa

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Question #5a3fa

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Answer 1 · 2017-04-10T03:32:52

2000K
(non rounded: 1638K)

Explanation:

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$ $(P_1V_1)/T_1=(P_2V_2)/T_2$

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.

$P_{1}$ $P_1$ -- 1 atm
$V_{1}$ $V_1$ -- 0.03 Liters
$T_{1}$ $T_1$ -- 273 Kelvin, 0˚C + 273= Kelvin

$P_{2}$ $P_2$ -- 3 atm: 1 atm = 760 mmHg $\frac{2280 m m H g}{760} = 3 a t m$ $(2280mmHg)/760= 3 atm$
$V_{2}$ $V_2$ -- 0.06 Liters
$T_{2}$ $T_2$ -- We will solve for this as a variable

$\frac{.03 \times 1}{273} = \frac{3 \times 0.06}{x}$ $[.03xx 1]/273=[3 xx 0.06)/x$ 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

Answer 2 · 2017-04-10T03:54:07

Use the combined gas law for this question.

The final temperature will be $\approx 2000 K$ $~~"2000 K"$ .

Explanation:

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

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$ $(P_1V_1)/T_1=(P_2V_2)/T_2$

where $P_{1}$ $P_1$ is the initial pressure in kilopascals (kPa), $V_{1}$ $V_1$ is the initial volume, $T_{1}$ $T_1$ is the initial temperature in Kelvins, $P_{2}$ $P_2$ is the final pressure in kPa, $V_{2}$ $V_2$ is the final volume, and $T_{2}$ $T_2$ 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 $0^{\circ} C$ $0^@"C"$ , or $273.15 K$ $"273.15 K"$ for gas laws. Pressure is $10^5 Pa$ $"10^5 Pa"$ or $100 kPa$ $"100 kPa"$ . The pressure needs to be converted from $mmHg$ $"mmHg"$ to $kPa$ $"kPa"$ .

List what is known/given:
$P_{1} = 100 kPa$ $P_1="100 kPa"$
$V_{1} = 30 mL$ $V_1="30 mL"$
$T_{1} = 273.15 K$ $T_1="273.15 K"$
$P_2=2280color(red)cancel(color(black)("mmHg"))xx(1 "kPa")/(7.50061561303color(red)cancel(color(black)("mmHg")))="303.9750492 kPa"$
$V_2="60 mL"$

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.

$T_2=(P_2V_2T_1)/(P_1V_1)$

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

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