What happens to the density of a gas when its volume decreases constant temperature and pressure?

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Temperature can be measured using the Celsius and Kelvin scales. Gas pressure increases with temperature. Equations explain the relationship between pressure, temperature and volume in gases.

By Serm Murmson

The combined gas law is an equation that relates the pressure, temperature and volume of a gas. Based on this equation, you can predict what will happen to a sample of gas if you change one of the variables. If you decrease pressure and temperature simultaneously, you will not know the exact result unless you know the exact values by which each quantity decreased.

The combined gas law is a combination of Boyle's law and Charles's law. Boyle's Law states that the volume of a gas held at constant temperature is inversely proportional to its pressure. Charles's law states that the volume of a gas held at constant pressure is directly proportional to its temperature in Kelvins. The combined gas law is the combination of these two relationships into one equation.

The combined gas law states that the pressure of a gas is inversely related to the volume and directly related to the temperature. If temperature is held constant, the equation is reduced to Boyle's law. Therefore, if you decrease the pressure of a fixed amount of gas, its volume will increase. However, if you were to maintain a constant volume while decreasing pressure, the temperature would also have to decrease. The relationship of gases at a constant volume is given by Gay-Lussac's law. Gay-Lussac's law states that at constant volume, the pressure and temperature of a gas are directly proportional.

If you decrease the temperature of a fixed amount of gas at constant pressure, the combined gas law reduces to Charles's law. In this case, volume will also decrease. If you were to maintain a constant volume while decreasing the temperature, the pressure would also have to decrease in order to satisfy Gay-Lussac's law.

If you decrease both the pressure and temperature of a fixed amount of gas, any changes you observe will be in the volume of the gas. Temperature is directly related to volume, and pressure is inversely related to volume. Therefore, the resulting changes in volume will depend on the quantitative changes in both pressure and temperature. For example, if you decrease the temperature of the gas by a greater degree than the decrease in pressure, the volume will decrease. However, if you decrease the pressure by a greater degree than the decrease in temperature, the volume will increase.

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.

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