What happens to the density of a gas as its volume increases at constant pressure and temperature?

Question 5 Short/Long Answer Questions

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Answer:

Solution:

As the temperature increases, volumes of most of the liquids also increases and when the volume increases density decreases. Similarly, when temperature decreases, the volume of most liquids decreases which increases the density. However, water shows anomalous behaviour. Water has maximum volume at 4-degree Celsius and maximum density at 4-degree Celsius.

But when water is cooled down further its volume starts increasing and hence, the density of water decreases when cooled further below than 4-degree celsius.

Hence, the density of water is maximum at 4-degree Celsius at 1\ g\ cm^{-3} or 1000\ kg\ m^{-3}

Video transcript

"Hello students, welcome tornado learning question and answer video. We have an interesting question over here. How does the density of a liquid or gas vary with temperature? So is it increase the temperature what will happen with identity between the degrees of temperature what will happen to the density but before going there we should know what we mean by the degree, right? So let's say density of any substance is equal to Mars. I must tell you next one is defined with this first make note of this because this is very important. And this is what we will use to find out they are supposed to taste the liquid molecules. Now let's get some heat. So I let me make a burner here. This is my burner. Now, I start picking the molecules. So I am giving heat to the Wall Street or hand hitting the Olympics what happens when I give heat to the different the temperature will increase so when the temperature increases or when I make the temperature rise, so what happens is the liquid. Or so now what is the link we fight because the molecules will start behaving like this so they will start moving further and further and help expand or the volume will increase When the volume increases what will happen to the dentist the family of the victim or the supervisor for heresy handsome. So if the density is mass upon wondering its volume increases density is inversely proportional to the border, right? It wasn't increases in density will decrease so in case of liquid the density Decreases Increase in temperature, but we have an exception to this now. Let's talk about exception. Which liquid do you think is the exception yet? It is our very own water. So water behaves in an anomalous has a very peculiar what the hell's maximum volume. So let's say this is no experiment me that maximum. The water is at maximum volume is at 4 degrees Celsius and maximum density is at 4 degrees Celsius, but then when we cool the water or when we lower the temperature of water when we lower the temperature of water what will happen. So if temperature was increasing your volume was increasing himself. To be able to do this right but now when we lower the temperature cool the water further the volume starts increasing so in water, it happens the reverse that doesn't mean use the temperature volume start engraving and it keeps on increasing and the density of water increases and then decreases right? We saw that from here. So when the volume increases so density will decrease right? Right. So the water doesn't city of water decreases when pools further below 100 degrees celsius if you cool the water below 4 degrees Celsius, the density will decrease and in fact, that is the reason why I always a solid but it floats on water this property of water helps high school float on water to the density of Ice is actually less than that, of course. So this is just an exception. However, for most of the liquid this whole into orbit a that when we increase the temperature the density decreases and when we decrease the temperature the density increases, but will follow for most of the latest apart from what is this that is our exception. I hope this point was here. Thank you. "

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The density will increase since the area will become smaller so gaseous particles will be close to each other making it more dense

Before doing any calculation, try to predict what you expect to happen to the density of a gas if pressure is increased while temperature is kept constant.

As you know, density is defined as the mass per unit of volume. Since the mass of the gas is also kept constant, the only way to change its density is to change the volume it occupies.

Now, what happens to the volume of an ideal gas when pressure is increased at constant temperature and number of moles?

You should remember from Boyle's Law that pressure and volume have an inverse relationship when temperature and number of moles of gas are kept constant.

What that tells you is that increasing the pressure of the gas will cause its volume to decrease. Likewise, decreasing the pressure of the gas will cause its volume to increase.

So right from the start you can say that since the pressure of the gas is increased, the volume will decrease, which in turn will cause the density of the gas to increase, since now you have the same mass of gas in a smaller volume.

If you start with #P_1# and #V_1# as the pressure and volume of the gas at an initial state, you can use Boyle's Law to write

#color(blue)(P_1 * V_1 = P_2 * V_2) -># the equation tha describes Boyle's Law

Here #P_2# and #V_2# are the pressure and volume of the gas at final state.

In your case, the pressure is doubled, so you can say that

#P_2 = 2 * P_1#

Plug this into the equation and solve for #V_2#

#V_2 = P_1/P_2 * V_1#

#color(purple)(V_2) = color(red)(cancel(color(black)(P_1)))/(2color(red)(cancel(color(black)(P_1)))) * V_1 = color(purple)( 1/2 * V_1)#

The density of the gas at the initial state was

#rho_1 = m/V_1" "#, where

#m# - the mass of gas

The density of the gas at the final state will be

#rho_2 = m/color(purple)(V_2) = m * 1/(color(purple)(1/2 * V_1)) = 2 * overbrace(m/V_1)^(color(red)(=rho_1))#

Therefore,

#rho_2 = color(green)(2 * rho_1)#

So, you can now say that doubling the pressure of the gas will halve its volume, which in turn will double its density.