A substance consisting only of Na, B and H is 60.80% Na and 28.60% B. What is the empirical formula of the substance?

Question

Luna Chen · Accepted Answer

#NaBH_4#

As is standard with these sorts of problems, we assume a #100*g# mass of compound to calculate the empirical formula:

#Na: (60.80*g)/(22.99*g*mol^-1)# #=# #2.65*mol#

#B: (28.60*g)/(10.81*g*mol^-1)# #=# #2.65*mol#

#H: (10.60*g)/(1.00794*g*mol^-1)# #=# #10.52*mol#

And then we divide thru each mass by the ATOMIC mass of each constituent to give a molar ratio.

How did I know that there were #10.6*g# hydrogen? The question did not give me this percentage composition.

And now we divide thru by the smallest molar quantity, i.e. #2.65*mol#, to give an empirical formula of:

#NaBH_4#

This is sodium borohydride, a very common laboratory reagent.

Luna Chen · Answer

undefined The empirical formula of the substance is Na₂B₄H₈.

Avery Adams · Answer

undefined To find the empirical formula of the substance, we need to determine the ratio of each element in the compound based on the given percentages.

1. Convert the percentages to grams:
   - $ 60.80\% $ Na means $ 60.80 $ grams of Na in a $ 100 $ gram sample.
   - $ 28.60\% $ B means $ 28.60 $ grams of B in a $ 100 $ gram sample.

2. Determine the number of moles for each element:
   - Moles of Na = $ \frac{60.80 \, \text{g}}{22.99 \, \text{g/mol}} $
   - Moles of B = $ \frac{28.60 \, \text{g}}{10.81 \, \text{g/mol}} $

3. Find the ratio of moles of each element by dividing by the smallest number of moles.

4. The ratio of moles gives us the subscripts for the empirical formula.

Given the moles, we find that the ratio of Na to B is approximately 2.81:2.65, or approximately 1.06:1.

Thus, the empirical formula of the substance can be approximated as $ \text{NaB} $.