A 20.0 -L tank contains 4.86 ×10^-4 kg of helium at 18.0^∘ C . The molar mass of helium is 4.00

A 20.0 -L tank contains 4.86 ×10^-4 kg of helium at 18.0^∘ C...

Key Concepts

Pressure Unit Conversion

Pressure unit conversion is important when the calculated pressure needs to be expressed in different units for consistency and comparison. Understanding that one atmosphere is equivalent to approximately 101,325 pascals allows conversion between these units, making it easier to communicate and interpret experimental and theoretical results.

Temperature Conversion

Temperature conversion is essential in gas law calculations because the ideal gas law requires temperature to be in Kelvin rather than Celsius. Converting from Celsius to Kelvin, by adding 273.15, ensures that the temperature variable is in the absolute scale, which is necessary for accurate calculations using gas laws.

Moles and Molar Mass

This concept describes the calculation of the amount of substance (measured in moles) by dividing the mass of the substance by its molar mass. It is a fundamental conversion in chemistry that allows us to translate a measured mass into a count of particles, which is particularly useful when dealing with macroscopic amounts of material in chemical and physical calculations.

Ideal Gas Law

The ideal gas law, represented by the equation PV = nRT, establishes a relationship between pressure, volume, number of moles, temperature, and the universal gas constant. This law is crucial for predicting the behavior of gases under various conditions assuming ideal behavior, allowing one to solve for any one variable when the others are known.

Transcript

00:01 So there is a tank of 20 liters so volume of the tank is equal to 20 liters so let me write this in si that is in meter cube so that will be 20 into 10 to the power minus 3 meter cube so this is a volume of a tank and it contains certain amount of helium gas so let me write that as mass m small m to be 4 .86 into 10 to power minus 4 kg the temperature at which the gas exists in the tank is 18 degrees celsius so to convert this into si you know the si unit of temperature is kelvin so you add 18 and to 73 so this should give me a temperature in kelvin that comes out to 2 .91 kelvin.

01:02 So the molar mass of helium, let me denote that by capital m.

01:07 The molar mass capital m is given as 4 gram per mole.

01:15 Now if you write this in si, that should be 4 into 10 to the power minus 3 kg per mole.

01:24 So one mole of helium is equal to 4 .2 .2.

01:30 Kggy now the question asks us how many moles of helium are there in the tank number of moles n is equal to what so just use the question says that one of the question says that here one of the helium is this much kazi so we have this much cases of helium so it's just a simple unit method to determine how many moles is equivalent to this casey right so we use number of moles will be equal to the mass of total mass of the helium gas divided by the molecular weight of the helium gas so if you plug these values in here that will be 4 .86 into 10 to the power minus 4 upon 4 into 10 to the power minus 3 so this will give us the number of most that will be 0 .122 moles so this much more of helium gas is inside the tank now the next question b asks us to calculate the pressure in the tank so we have the number of moles we have the volume we have the temperature you should have got an idea that a simple ideal equation ideal gas equation is equal to an rt can be used to determine p where r is the universal gas constant which value is given by given as 8 .314 jule per mole per kelvin so from this expression we can write p is equal to nr t by v now we know the values for all these parameters you know the value of n we know the value of r we know the value of t and we know the value of volume so just calculate this you get the answer to be 14758 .18.

04:00 Now the si unit of pressure is pascal.

04:03 So pa...

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