Question #fd627

1 Answer
Jul 30, 2017

8xx10^238×1023 "protons "protons (one significant figure)

Explanation:

We're asked to find the number of nucleic protons in 22 "g CH"_4g CH4.

To do this, we can first use the molar mass of methane to convert from grams to moles:

2cancel("g CH"_4)((1color(white)(l)"mol CH"_4)/(16.04cancel("g CH"_4))) = color(red)(0.1247 color(red)("mol CH"_4

Now, we can use Avogadro's number to convert from moles to molecules of methane:

color(red)(0.1247)cancel(color(red)("mol CH"_4))((6.022xx10^23color(white)(l)"molecules CH"_4)/(1cancel("mol CH"_4)))

= color(green)(7.508xx10^22 color(green)("molecules CH"_4

Finally, we use the atomic number of each element to find the total number of protons; we know:

"carbon" = 6

"hydrogen" = 1 xx overbrace(4)^"four atoms per molecule" = 4

For a total of

6+4=ul(10 "protons"

per molecule.

Therefore,

color(green)(7.508xx10^22)cancel(color(green)("molecules CH"_4))((10color(white)(l)"protons")/(1cancel("molecule CH"_4))) = color(blue)(ul(8xx10^23color(white)(l)"protons"

rounded to 1 significant figure.