Question #67d87

1 Answer
Jun 12, 2017

1.2xx10^71.2×107 "g H"_2g H2

Explanation:

We're asked to find the mass, in "g"g, of a sample of hydrogen gas containing 3.5 xx 10^303.5×1030 hydrogen molecules.

To convert from particles to moles, we can use Avogadro's number, 6.022xx10^23"particles"/"mol"6.022×1023particlesmol.

After this conversion, we can use the molar mass of "H"_2H2, which is

overbrace(2)^("two atoms of H per molecule") xx overbrace(1.01"g"/"mol")^"molar mass of H" = color(red)(2.02"g"/"mol"

to convert from moles to grams.

(The number 1.01"g"/"mol" is the same number as the relative atomic mass of hydrogen, 1.01 "amu", which on most periodic tables can be found directly beneath the element's symbol.)

Converting from molecules to moles, we have

3.5 xx 10^30cancel("molecules H"_2)((1"mol H"_2)/(6.022xx10^23cancel("molecules H"_2)))

= color(blue)(5.8xx10^6 color(blue)("mol H"_2

Now, using the molar mass, let's convert from moles to grams:

color(red)(5.8xx10^6 cancel(color(red)("mol H"_2))((2.02"g H"_2)/(1cancel("mol H"_2)))

= color(purple)(1.2xx10^7 color(purple)("g H"_2

rounded to 2 significant figures, the amount given in the problem.

Therefore, 3.5xx10^30 molecules of "H"_2 has a mass of color(purple)(1.2 xx 10^7 grams.