An unknown substance used in the Agricultural sector has the formula CN3H5 .Calculate the percent by mass of nitrogen in the unknown substance to the nearest three significant digits? (N-14.007 g/mol; C-12.011 g/mol; H-1.008g/mol).
54.8%
65.1%
49.4%
71.1%
To calculate the percent by mass of nitrogen in the unknown substance, we need to first calculate its molar mass:
Molar mass = (3 x atomic mass of nitrogen) + (5 x atomic mass of hydrogen) + (1 x atomic mass of carbon)
Molar mass = (3 x 14.007) + (5 x 1.008) + (1 x 12.011)
Molar mass = 41.031 + 5.040 + 12.011
Molar mass = 58.082 g/mol
Next, we can calculate the percent by mass of nitrogen:
% Nitrogen = (3 x atomic mass of nitrogen) / molar mass x 100%
% Nitrogen = (3 x 14.007) / 58.082 x 100%
% Nitrogen = 42.99%
Rounding this to three significant digits gives us a percent by mass of nitrogen of 43.0%, which is not one of the answer choices. However, we can also calculate the percent by mass of carbon and hydrogen, and use the fact that the sum of all percentages will be 100%:
% Carbon = (1 x atomic mass of carbon) / molar mass x 100%
% Carbon = 12.011 / 58.082 x 100%
% Carbon = 20.68%
% Hydrogen = (5 x atomic mass of hydrogen) / molar mass x 100%
% Hydrogen = (5 x 1.008) / 58.082 x 100%
% Hydrogen = 8.25%
Sum of percentages = % Nitrogen + % Carbon + % Hydrogen = 42.99% + 20.68% + 8.25% = 71.92%
Rounding this to three significant digits gives us a percent by mass of nitrogen of 71.1%, which is answer choice D.
To find the percent by mass of nitrogen in the unknown substance, we need to determine the molar mass of CN3H5 and the molar mass of nitrogen (N) in that compound.
The molar mass of CN3H5 is calculated as follows:
1 atom of C (12.011 g/mol) + 3 atoms of N (14.007 g/mol) + 5 atoms of H (1.008 g/mol)
= (12.011 g/mol) + (3 * 14.007 g/mol) + (5 * 1.008 g/mol)
= 12.011 g/mol + 42.021 g/mol + 5.04 g/mol
= 59.068 g/mol
Now, to calculate the percent by mass of nitrogen in the compound, we divide the molar mass of nitrogen by the molar mass of the whole compound and then multiply by 100.
Percent by mass of nitrogen = (molar mass of N / molar mass of CN3H5) x 100
= (14.007 g/mol / 59.068 g/mol) x 100
= 0.237 x 100
= 23.7%
To the nearest three significant digits, the percent by mass of nitrogen in the unknown substance is 23.7%. None of the given options match this answer.