Math / Data & Statistics

QuestionThe data represents a sample of gas that has a constant volume and number of particles. Use the data to answer these two questions.
When the Kelvin temperature of the gas is tripled (increased by a factor of three), the pressure of \begin{tabular}{|c|c|c|} \hline Trial & \begin{tabular}{c} Temperature \\ $(\mathbf{K})$ \end{tabular} & \begin{tabular}{c} Pressure \\ (atm) \end{tabular} \\ \hline 1 & 200 & 0.80 \\ \hline 2 & 300 & 1.20 \\ \hline 3 & 400 & 1.60 \\ \hline 4 & 600 & 2.40 \\ \hline 5 & 800 & 3.20 \\ \hline \end{tabular} the gas becomes $\qquad$ Whoa! Not possible to tell

Studdy Solution

STEP 1

What is this asking? If we triple the temperature of some gas (keeping other stuff constant), what happens to the pressure? Watch out! Don't forget, the temperature must be in Kelvin!

STEP 2

1. Check if the data follows Gay-Lussac's Law
2. Calculate the pressure change factor
3. Calculate the new pressure

STEP 3

Gay-Lussac's Law says that if the volume and amount of gas are constant, the pressure and temperature are directly proportional.
This means if we double the temperature, we double the pressure.
If we triple the temperature, we triple the pressure!
Mathematically, this can be written as $P_1/T_1 = P_2/T_2$ .
Let's see if our data follows this law.

STEP 4

Let's pick two rows from our table and plug the values into the formula.
Let's try Trial 1 and Trial 2.
From Trial 1, we have $P_1 =$ 0.80 atm and $T_1 =$ 200 K.
From Trial 2, we have $P_2 =$ 1.20 atm and $T_2 =$ 300 K.

STEP 5

Plugging in the values, we get $\frac{0.80}{200} = \frac{1.20}{300}$ .
Simplifying both sides, we get $0.004 = 0.004$ .
Awesome! It works!
Let's try another pair just to be sure.

STEP 6

Let's use Trial 3 and Trial 5.
From Trial 3, $P_3 =$ 1.60 atm and $T_3 =$ 400 K.
From Trial 5, $P_5 =$ 3.20 atm and $T_5 =$ 800 K.

STEP 7

Plugging in, we get $\frac{1.60}{400} = \frac{3.20}{800}$ .
Simplifying, we get $0.004 = 0.004$ .
Perfect! It works again!
So, our data definitely follows Gay-Lussac's Law.

STEP 8

Since the temperature is tripling, and pressure and temperature are directly proportional, the pressure will also triple!
This means the pressure change factor is 3.

STEP 9

Let's pick a trial and triple the temperature.
Let's use Trial 1, where the temperature is 200 K and the pressure is 0.80 atm.
Tripling the temperature gives us $200 \cdot 3 =$ 600 K.

STEP 10

Since the pressure change factor is 3, the new pressure will be $0.80 \cdot 3 =$ 2.40 atm.
Look! This matches Trial 4 in the table, where the temperature is 600 K and the pressure is 2.40 atm.
Amazing!

STEP 11

When the Kelvin temperature of the gas is tripled, the pressure of the gas also triples.

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Studdy Solution

STEP 1

What is this asking? If we triple the temperature of some gas (keeping other stuff constant), what happens to the pressure? Watch out! Don't forget, the temperature must be in Kelvin!

STEP 2

1. Check if the data follows Gay-Lussac's Law
2. Calculate the pressure change factor
3. Calculate the new pressure

STEP 3

STEP 4

Let's pick two rows from our table and plug the values into the formula.
Let's try Trial 1 and Trial 2.
From Trial 1, we have $P_1 =$ 0.80 atm and $T_1 =$ 200 K.
From Trial 2, we have $P_2 =$ 1.20 atm and $T_2 =$ 300 K.

STEP 5

Plugging in the values, we get $\frac{0.80}{200} = \frac{1.20}{300}$ .
Simplifying both sides, we get $0.004 = 0.004$ .
Awesome! It works!
Let's try another pair just to be sure.

STEP 6

Let's use Trial 3 and Trial 5.
From Trial 3, $P_3 =$ 1.60 atm and $T_3 =$ 400 K.
From Trial 5, $P_5 =$ 3.20 atm and $T_5 =$ 800 K.

STEP 7

Plugging in, we get $\frac{1.60}{400} = \frac{3.20}{800}$ .
Simplifying, we get $0.004 = 0.004$ .
Perfect! It works again!
So, our data definitely follows Gay-Lussac's Law.

STEP 8

Since the temperature is tripling, and pressure and temperature are directly proportional, the pressure will also triple!
This means the pressure change factor is 3.

STEP 9

Let's pick a trial and triple the temperature.
Let's use Trial 1, where the temperature is 200 K and the pressure is 0.80 atm.
Tripling the temperature gives us $200 \cdot 3 =$ 600 K.

STEP 10

Since the pressure change factor is 3, the new pressure will be $0.80 \cdot 3 =$ 2.40 atm.
Look! This matches Trial 4 in the table, where the temperature is 600 K and the pressure is 2.40 atm.
Amazing!

STEP 11

When the Kelvin temperature of the gas is tripled, the pressure of the gas also triples.

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Studdy Solution

STEP 1

What is this asking? If we triple the temperature of some gas (keeping other stuff constant), what happens to the pressure? Watch out! Don't forget, the temperature must be in Kelvin!

STEP 2

1. Check if the data follows Gay-Lussac's Law2. Calculate the pressure change factor3. Calculate the new pressure

STEP 3

STEP 4

Let's pick two rows from our table and plug the values into the formula.Let's try Trial 1 and Trial 2.From Trial 1, we have P1=P_1 = P1​= **0.80 atm** and T1=T_1 = T1​= **200 K**.From Trial 2, we have P2=P_2 = P2​= **1.20 atm** and T2=T_2 = T2​= **300 K**.

STEP 5

Plugging in the values, we get 0.80200=1.20300\frac{0.80}{200} = \frac{1.20}{300}2000.80​=3001.20​.Simplifying both sides, we get 0.004=0.0040.004 = 0.0040.004=0.004.Awesome! It works!Let's try another pair just to be sure.

STEP 6

Let's use Trial 3 and Trial 5.From Trial 3, P3=P_3 = P3​= **1.60 atm** and T3=T_3 = T3​= **400 K**.From Trial 5, P5=P_5 = P5​= **3.20 atm** and T5=T_5 = T5​= **800 K**.

STEP 7

Plugging in, we get 1.60400=3.20800\frac{1.60}{400} = \frac{3.20}{800}4001.60​=8003.20​.Simplifying, we get 0.004=0.0040.004 = 0.0040.004=0.004.Perfect! It works again!So, our data definitely follows Gay-Lussac's Law.

STEP 8

Since the temperature is tripling, and pressure and temperature are directly proportional, the pressure will also triple!This means the pressure change factor is **3**.

STEP 9

Let's pick a trial and triple the temperature.Let's use Trial 1, where the temperature is **200 K** and the pressure is **0.80 atm**.Tripling the temperature gives us 200⋅3=200 \cdot 3 = 200⋅3= **600 K**.

STEP 10

Since the pressure change factor is **3**, the new pressure will be 0.80⋅3=0.80 \cdot 3 = 0.80⋅3= **2.40 atm**.Look! This matches Trial 4 in the table, where the temperature is **600 K** and the pressure is **2.40 atm**.Amazing!

STEP 11

When the Kelvin temperature of the gas is tripled, the pressure of the gas also triples.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Check if the data follows Gay-Lussac's Law
2. Calculate the pressure change factor
3. Calculate the new pressure

Let's pick two rows from our table and plug the values into the formula.
Let's try Trial 1 and Trial 2.
From Trial 1, we have $P_1 =$ 0.80 atm and $T_1 =$ 200 K.
From Trial 2, we have $P_2 =$ 1.20 atm and $T_2 =$ 300 K.

Plugging in the values, we get $\frac{0.80}{200} = \frac{1.20}{300}$ .
Simplifying both sides, we get $0.004 = 0.004$ .
Awesome! It works!
Let's try another pair just to be sure.

Let's use Trial 3 and Trial 5.
From Trial 3, $P_3 =$ 1.60 atm and $T_3 =$ 400 K.
From Trial 5, $P_5 =$ 3.20 atm and $T_5 =$ 800 K.

Plugging in, we get $\frac{1.60}{400} = \frac{3.20}{800}$ .
Simplifying, we get $0.004 = 0.004$ .
Perfect! It works again!
So, our data definitely follows Gay-Lussac's Law.

Since the temperature is tripling, and pressure and temperature are directly proportional, the pressure will also triple!
This means the pressure change factor is 3.

Let's pick a trial and triple the temperature.
Let's use Trial 1, where the temperature is 200 K and the pressure is 0.80 atm.
Tripling the temperature gives us $200 \cdot 3 =$ 600 K.

Since the pressure change factor is 3, the new pressure will be $0.80 \cdot 3 =$ 2.40 atm.
Look! This matches Trial 4 in the table, where the temperature is 600 K and the pressure is 2.40 atm.
Amazing!