By rearranging the ideal gas law, we can establish direct and inverse relationships between its variables. So here we have the ideal gas law formula, which is pv = nrt. R is our gas constant. Because it's constant, we don't have to relate it to the other variables. Next, we have our variable chart and we'll see what effect happens to the other variables if pressure is increasing and volume is increasing. And then in our variable relationships we'll take a look at different pairs of variables and see whether they are directly proportional or inversely proportional to one another. Alright. So first, let's look at what happens when I increase pressure. Let's see what is the effect that it has on volume. Our equation is pv = nrt. We're not gonna talk about n r t because we're looking strictly at the relationship between pressure and volume. Now to make them relate to one another, we're gonna say that this is equal to a constant, let's just say that it's 1, and we're gonna bring volume over to the other side. By doing that, we can see that the relationship is that pressure is equal to 1 / v. Pressure here is a numerator, volume is a denominator. If you've watched my other videos in terms of direct and inverse relationships, realize that because they're on different levels, they're inversely proportional. If volume is increasing and the top is staying constant, if volume is increasing that means pressure would be decreasing. If volume is decreasing, pressure would be increasing. So coming back to our variables chart we're gonna say that the relationship is if we increase my pressure that's gonna decrease my volume because they have an inversely proportional relationship or opposite relationship. Now let's compare pressure and moles. Okay. So pressure and moles, ignore volume r and t. So then this would just be pressure equals moles. They're both numerators, both on the same level. If I increase 1 that's gonna cause an increase in the other. So increasing pressure while keeping all the other variables out increases my moles. Since they're increasing or decreasing together, they are directly proportional. Next, pressure equals temperature. Right? Ignore volume, moles, and r because we're focusing only on pressure and temperature. Again, they're both numerators so they both increase together. So they are directly proportional. Alright. Now that we've done that let's look at volume. So volume, we're increasing volume and we're trying to see what effect it has on my moles and my temperature here. So focus on only moles and volume. Ignore pressure, ignore r and t. Volume and moles are on the same level with one another. They're both numerators, so increasing one would cause an increase in the other. Why? Because they are directly proportional. And then finally, volume equals temperature. So at this point, you've seen us do the other ones. Give yourself a second pause in the video if you want and see what the relationship between volume and temperature would be. Alright. Hopefully you've done that and realize that volume and temperature, both of them considered numerators, both on the same level, an increase in one will cause an increase in the other. Why? Because they too would be directly proportional. So these are the relationships that we can establish with the variables of the ideal gas law. And we can see that really only pressure and volume is where we would see an inverse relationship when doing these pairings of the variables. So keep this in mind if you're faced with any type of theoretical question where they're increasing or decreasing one variable and asking for the effect on another within the ideal gas law.

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# The Ideal Gas Law Applications - Online Tutor, Practice Problems & Exam Prep

The ideal gas law, represented as ${p}^{v}=nRT$, establishes relationships among pressure, volume, moles, and temperature. Pressure and volume are inversely proportional, while pressure and moles, as well as pressure and temperature, are directly proportional. Similarly, volume is directly proportional to both moles and temperature. Understanding these relationships is crucial for solving theoretical problems in gas behavior.

The **Ideal Gas Law Applications** establish both the direct and inverse relationships between the Ideal Gas Law variables.

## Understanding the Ideal Gas Law Applications

### The Ideal Gas Law Applications

#### Video transcript

### The Ideal Gas Law Applications Example 1

#### Video transcript

If the number of moles n inside a container were tripled while keeping the pressure p constant, what will happen to the volume v? Alright. So in this question, they're telling us that our pressure is being held constant, so just ignore it. What's changing are our moles, and we have to understand what effect that will have on my volume. Looking at the ideal gas law, pv=nrt, we're only paying attention to volume and moles. The other variables we can remove. By doing that, we see that it simplifies further into v=n. So this means that volume and moles have a direct relationship to each other; they're directly proportional. Meaning, whatever happens to one, the same thing happens to the other. Since our moles are being tripled, that would mean that my volume would also have to be tripled. This means the answer would have to be option C. So again, sometimes you'll be faced with questions like this where you're not given actual numbers, but you have to understand the direct or possibly inverse relationship between a pair of variables from the ideal gas law.

The relationship between the partial pressure of a gas (P) and the number of moles of that gas (n) is best represented by which of the following graphs?

## Do you want more practice?

### Here’s what students ask on this topic:

What is the ideal gas law and how is it used?

The ideal gas law is a fundamental equation in chemistry and physics that describes the behavior of an ideal gas. It is represented as $pv=nRT$, where $p$ is pressure, $v$ is volume, $n$ is the number of moles, $R$ is the gas constant, and $T$ is temperature. This law is used to calculate any one of these variables if the others are known, making it essential for solving problems related to gas behavior in various scientific fields.

How are pressure and volume related in the ideal gas law?

In the ideal gas law, pressure and volume are inversely proportional to each other. This means that if the pressure of a gas increases, its volume decreases, and vice versa, provided the number of moles and temperature remain constant. Mathematically, this relationship is expressed as $pv=k$, where $k$ is a constant. This inverse relationship is crucial for understanding how gases behave under different conditions.

What is the relationship between pressure and temperature in the ideal gas law?

In the ideal gas law, pressure and temperature are directly proportional to each other when the volume and number of moles are held constant. This means that if the temperature of a gas increases, its pressure also increases, and vice versa. This relationship is expressed as $p=kT$, where $k$ is a constant. Understanding this direct proportionality helps in predicting how changes in temperature affect gas pressure.

How do you calculate the number of moles using the ideal gas law?

To calculate the number of moles using the ideal gas law, you can rearrange the equation $pv=nRT$ to solve for $n$. The rearranged equation is $n=\frac{pv}{RT}$. By knowing the values of pressure, volume, the gas constant, and temperature, you can substitute these into the equation to find the number of moles of the gas.

What is the significance of the gas constant (R) in the ideal gas law?

The gas constant, denoted as $R$, is a crucial component of the ideal gas law. It provides the proportionality factor that relates the other variables (pressure, volume, moles, and temperature) in the equation $pv=nRT$. The value of $R$ depends on the units used for pressure, volume, and temperature. Commonly, $R$ is 8.314 J/(mol·K) when using SI units. It ensures that the equation is dimensionally consistent and allows for accurate calculations of gas properties.

How does the ideal gas law explain the behavior of gases under different conditions?

The ideal gas law explains the behavior of gases by establishing relationships among pressure, volume, moles, and temperature. It shows that pressure and volume are inversely proportional, while pressure and temperature, as well as volume and temperature, are directly proportional. These relationships help predict how a gas will respond to changes in one variable when the others are held constant. For example, increasing the temperature of a gas will increase its pressure if the volume is constant. This law is fundamental for understanding gas behavior in various scientific and engineering applications.

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