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Find the RMS speed of #"H"_2# at #"273.15 K"# and #"293.15 K"#? The density at STP is #"0.08988 g/L"#.

Answer 1

Caleb Adams

The density given doesn't matter. The RMS speed is:

#v_(RMS) = sqrt((3RT)/M)#

where #R# is the universal gas constant in energy units, #T# is in #"K"#, and #M# is the molar mass in #"kg/mol"#.

Since you are given the temperatures, and since density varies with temperature anyway, ignore the density.

#color(blue)(v_(RMS1)) = sqrt((3RT_1)/M)#

#= sqrt((3cdot"8.314472 kg"cdot"m"^2"/s"^2"/mol"cdot"K" cdot "273.15 K")/("0.0028014 kg/mol"))#

#=# #color(blue)("1560 m/s")#

#color(blue)(v_(RMS2)) = sqrt((3RT_2)/M)#

#= sqrt((3cdot"8.314472 kg"cdot"m"^2"/s"^2"/mol"cdot"K" cdot "293.15 K")/("0.0028014 kg/mol"))#

#=# #color(blue)("1620 m/s")#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.