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Cerrena [4.2K]
3 years ago
8

Prove that PV = nRT.​

Chemistry
1 answer:
qaws [65]3 years ago
6 0

Find your answer in the explanation below.

Explanation:

PV = nRT is called the ideal gas equation and its a combination of 3 laws; Charles' law, Boyle's law and Avogadro's law.

According to Boyle's law, at constant temperature, the volume of a gas is inversely proportional to the pressure. i.e V = 1/P

From, Charles' law, we have that volume is directly proportional to the absolute temperature of the gas at constant pressure. i.e V = T

Avogadro's law finally states that equal volume of all gases at the same temperature and pressure contain the same number of molecules. i.e V = n

Combining the 3 Laws together i.e equating volume in all 3 laws, we have

V = nT/P,

V = constant nT/P

(constant = general gas constant = R)

V = RnT/P

by bringing P to the LHS, we have,

PV = nRT.

Q.E.D

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The question is incomplete, complete question is :

In the Haber reaction, patented by German chemist Fritz Haber in 1908, dinitrogen gas combines with dihydrogen gas to produce gaseous ammonia. This reaction is now the first step taken to make most of the world's fertilizer. Suppose a chemical engineer studying a new catalyst for the Haber reaction finds that 348 liters per second of dinitrogen are consumed when the reaction is run at 205°C and 0.72 atm. Calculate the rate at which ammonia is being produced.

Answer:

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Explanation:

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Pressure of the gas = P = 0.72 atm

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n=\frac{PV}{RT}=\frac{0.72 atm\times 348 L}{0.0821 atm L/mol K\times 478 K}=6.385 mol

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217.08 grams of ammonia is produced per second.So, the rate of production of ammonia is 217.08 grams per second.

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