A quantity of CO gas occupies a volume of 0.48 L at 1.0 atm and 275 K. The pressure of the ga

step 1 I'm here to solve question number 132. A quantity of carbon monoxide gas occupied a volume of 0

A quantity of CO gas occupies a volume of 0.48 L at 1.0...

A quantity of CO gas occupies a volume of $0.48 \mathrm{~L}$ at $1.0 \mathrm{~atm}$ and $275 \mathrm{~K}$. The pressure of the gas is lowered and its temperature is raised until its volume is $1.3 \mathrm{~L}$. Determine the density of the CO under the new conditions.

Key Concepts

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, is a fundamental relationship for ideal gases that connects pressure (P), volume (V), number of moles (n), temperature (T), and the universal gas constant (R). This law provides the basis for understanding how a gas’s state variables change when any one of them is altered while the number of particles remains constant.

Gas Density Calculation

Gas density is defined as the mass of the gas per unit volume. In the context of an ideal gas, the density can be calculated by combining the ideal gas law with the definition of density (? = mass/volume) and substituting mass with the product of the number of moles and the molar mass. This leads to the useful formula ? = (P × M)/(R × T), which shows how density depends on pressure, molar mass, the gas constant, and temperature.

Molar Mass

Molar mass is the mass per mole of a substance and is a critical factor when determining the mass of a gas from its number of moles. In gas law problems, knowing the molar mass allows for the conversion between the amount of gas (in moles) and its corresponding mass, which is essential for computing density when using the formula derived from the ideal gas law.

Transcript

00:01 I'm here to solve question number 132.

00:07 A quantity of carbon monoxide gas occupied a volume of 0 .48 liter at 1 atmosphere, the pressure is 1 atmosphere.

00:24 And temperature is 275 ferrets.

00:30 The pressure of the gas is lower.

00:32 So we have p2, that is lower, and its temperature is raised.

00:39 We have t2 our this is done the gas has new follow new follow of 1 .3 later this is lower it is this is so we have new follow at this condition determine the density of carbon monoxide at this condition density we know is mass divided by following and we know mass is a cost of the gas with the constant but the volume is changing this is changing because the volume is changing that is why the density at the first condition is different from the density at this condition so what we need to know is the mass we already have the volume for to know the mass we need to know the mold that once we know the mold there we can get the the mold is also constant but once we know the more we can get the molecular mass of carbon monoxide so from there molecular mass so from there we get the mass so what my first approach is to find more i will use gas law pf equals nm rt to find the more i don't have all the parameters here so there is no way i can get there but the mold here is also the mole here so mold is constant so i will use the force all this value to get my mode so my n equals p v divided by r 2 so my n will be p is one atmosphere applied by v is 0 .48 liter and then my r is 0 .0 .082 you know is a constant temperature per cave and my temperature is 275 so if i do this it gives me my move i'm operating operating my calculator now 1 .0 .4 is divided by i open a bracket 0 .082 twice 275 that is that is 0 .0 .0 .0 .0 .0 .0 .0 .0 .0.

03:54 C0.

03:57 C0.

04:08 Cofo21 more...

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