Which of the following statements is(are) true? a. If the...

Which of the following statements is(are) true? a. If the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant b. If the temperature of a gas increases from $25^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C},$ the volume of the gas would double, assuming that the pressure and the number of moles of gas remain constant. c. The device that measures atmospheric pressure is called a barometer. d. If the volume of a gas decreases by one half, then the pressure would double, assuming that the number of moles and the temperature of the gas remain constant.

Which of the following statements is(are) true?
a. If the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant
b. If the temperature of a gas increases from $25^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C},$ the volume of the gas would double, assuming that the pressure and the number of moles of gas remain constant.
c. The device that measures atmospheric pressure is called a barometer.
d. If the volume of a gas decreases by one half, then the pressure would double, assuming that the number of moles and the temperature of the gas remain constant.

Key Concepts

Barometer

A barometer is an instrument specifically used to measure atmospheric pressure, which is essential in predicting weather patterns and understanding pressure variations in the atmosphere.

Charles's Law

Charles's law indicates that the volume of a gas is directly proportional to its absolute temperature (in Kelvin) when pressure and the amount of gas remain constant. Temperature increases will therefore yield increases in volume in accordance with this law.

Avogadro's Law

Avogadro's law states that, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles present. This means that increasing the number of moles causes a proportional increase in volume.

Boyle's Law

Boyle's law describes the inverse relationship between pressure and volume for a gas at constant temperature and fixed amount of gas. If the volume decreases, the pressure increases proportionately, and vice versa.

Transcript

00:01 And this problem we're given to determine whether or not statements are true or false.

00:06 In the first statement for a, we're given this statement, if the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant.

00:22 So if we think about our gas law, pv equals nrt, and we have that our volume and moles are the ones that we're considering changing and our gas constant temperature and pressure will be the same.

00:43 Then we can end up with an equation of v1 over n equals rt over p, which equals v, 2 over n2 now in this scenario we are saying that the number of moles is going to double and we're trying to figure out if the volume is going to double so if we take this equation since these are equal we can get rid of that middle portion so v1 over n1 equals v2 and since n2 equals twice the moles of the original n.

01:31 We can make that 2n.

01:32 Substitute that in as 2n.

01:35 And solving for this, solving for our volume, our v2, we can cross multiply.

01:42 So we have v1 times 2n1 equals v2 times n1.

01:49 Divide both sides by n, and you have v1.

01:55 So 2v1 equals 2v1, v2.

01:58 So yes, it is true.

02:00 If you double the number of moles, then the volume will also double.

02:06 All right.

02:08 B is saying, is asking, if the temperature of a gas increases from 25 degrees celsius to 50 degrees celsius, the volume of the gas would double, assuming the pressure and number of moles of the gas remain the same.

02:26 So we can do kind of the same thing.

02:28 So we can do kind of the same here as we did before, but in this case it would be v1 over t1 equals v2 over two times t1.

02:43 And we would get that yes, if the gas, when we solve for v2, we would end up having that two times our v1 will equal our v2.

02:57 If our gas doubles...

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