How many moles of hydrogen gas are produced when #"20 g"# of sodium metal react with #"10 g"# of water?

Question

Serenity Allen · Accepted Answer

#"0.6 g H"_2#

Write the balanced chemical equation describing this reaction first.

#"Na"_ ((s)) + color(blue)(2)"H"_ 2"O"_ ((l)) -> 2"NaOH"_ ((aq)) + "H"_ (2(g)) uarr#

Sodium and water react in a #1:color(blue)(2)# mole ratio, so the next thing to do here is to convert the given masses to moles by using the molar mass of sodium and the molar mass of water, respectively.

#20 color(red)(cancel(color(black)("g"))) * ("1 mole Na")/(23.0color(red)(cancel(color(black)("g")))) = "0.870 moles Na"#

#10 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "0.555 moles H"_2"O"#

Thus, for every mole of sodium to participate in the reaction, you need

#0.870 color(red)(cancel(color(black)("moles Na"))) * (color(blue)(2)color(white)(.)"moles H"_2"O")/(1color(red)(cancel(color(black)("mole Na")))) = "1.74 moles H"_2"O"#

You can observe that you have

#overbrace("0.555 moles H"_2"O")^(color(purple)("what is available")) " "< " "overbrace("1.74 moles H"_2"O")^(color(purple)("what is needed"))#

This indicates that water will function as a limiting reagent, meaning that before all of the sodium moles have an opportunity to participate in the reaction, it will be fully consumed.

So, you can say that the reaction will consume #0.555# moles of water.

To find the number of moles of hydrogen gas produced, use the #color(blue)(2):1# mole ratio that exists between water and hydrogen gas.

#0.555 color(red)(cancel(color(black)("moles H"_2"O"))) * "1 mole H"_2/(color(blue)(2)color(red)(cancel(color(black)("moles H"_2"O")))) = "0.2775 moles H"_2#

Lastly, use the hydrogen gas molar mass to convert this to grams.

#0.2775 color(red)(cancel(color(black)("moles H"_2))) * "2.016 g"/(1color(red)(cancel(color(black)("mole H"_2)))) = color(darkgreen)(ul(color(black)("0.6 g")))#

The number of significant figures (sig figs) you have for your values must be rounded to one in the answer.

Jose Ayala · Answer

undefined 2 moles of hydrogen gas are produced.