We're asked to find the number of nucleic protons in #2# #"g CH"_4#.
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.
