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Problem 1:

At $27^{\circ}C$ and $\frac{77}{76}atm$ pressure, how many moles of methane gas are present in $20L$ methane?

Using SI units:

$$n=\frac{PV}{RT}$$

$$n=\frac{101325\times\frac{77}{76}\times 20\times 10^{-3}}{8.314\times300}$$

$$n=0.8232\ (approx.)$$

Using $L,atm,K$:

$$n=\frac{PV}{RT}$$

$$n=\frac{\frac{77}{76}\times20}{0.082\times300}$$

$$n=0.8237\ (approx.)$$

Observation 1: Here the difference is slight $(0.0005)$, as mentioned by @josephh.

Problem 2:

At $20^{\circ}C$ and $740mm(Hg)$ pressure, $0.842g$ of a gas has $400mL$ volume. What is its molecular mass?

Using SI units:

$$M=\frac{wRT}{PV}$$

$$M=\frac{0.842\times 8.314\times 293}{\frac{740}{760}\times 101325\times 400\times 10^{-6}}$$

$$M=51.975\ (approx.)$$

Using $L, atm, K$:

$$M=\frac{wRT}{PV}$$

$$M=\frac{0.842\times 0.082\times 293}{740\times0.4}$$

$$M=51.942\ (approx.)$$

Observation 2: Here the difference is a bit more than the previous case $(0.033)$. Why are these differences emerging?

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    $\begingroup$ This is probably just due to rounding. Your only off by 0.0005. $\endgroup$
    – joseph h
    Commented Nov 11, 2021 at 6:39
  • $\begingroup$ With your input values as given, the answers the second question should be given as 52 for both cases. You only have two significant digits for your input values. And 0.82 for the first. There is no difference. $\endgroup$
    – nasu
    Commented Nov 11, 2021 at 12:37
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    $\begingroup$ Your question doesn’t get any better by extending it while ignoring the answer and the comments. There is nothing emerging; it’s simply GIGO (rather IIIO, I = Inaccurate) $\endgroup$ Commented Nov 11, 2021 at 17:40

1 Answer 1

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You are getting slightly different values because you input values slightly differ.

${101325\times 10^{-3}\over 8.314} \approx 12,18727 $

${1 \over 0.082} \approx 12.19512 $

Since your input values are only accurate to the second digit you cannot expect your answer being correct to the third digit.

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