Agaseous compound weighing 9.91582 g and occupying 1.312 x103 ml of volume at 98.7? c and 1023 torr of pressure is found by elemental analysis to be comprised of 6.2276 g c, 1.25382 g h, and 2.4344 g n – what is its molecular formula?

Molecular formula = C9H6N3

Explanation:

1. We have to change grams to mol:

C:

1 mol C = 12 g

6.2276 g C ×(1mol/ 12g)= 0.519 mol C

H:

1 mol H = 1 g

1.25382 g H ×(1mol / 1g)= 1.254 mol H

N:

1 mol N = 14 g

2.4344 g N ×(1mol/14 g)= 0.174 mol N

2. Then, you have to divide by smallest number of moles, it is 0.174. You have to approximate the values to integer numbers:

C:

0.519 mol C / 0.174 = 2.983 = 3

H:

1.254 mol H/ 0.174= 1.460 = 2

N:

0.174 mol N/0.174= 1

With this numbers, we obtain the empirical formula C3H2N. Now we gonna calcualte the molecular formula with the empirical formula:

3. Find the molecular weith of empirical formula:

C3 = 12 x 3 = 36

H = 2

N = 14

C3H2N = 36 +2 +14 =52 g/mol

4. Then you have to divide the molecular formula molar mass over the empirical formula mass:

molecular formula molar mass / empirical formula molar mass

To find the molecular formula mass we have to use the ideal gas equation:

PV=nRT

Where:

P= 1023 torr

V = 1.312 ×103 mL

n = mol

R = 0.0821 atmL /molK

T = 98.7 °C

Remeber you have to use the right units for the data, so we gonna change torr to atm, and mL to L and °C to K:

P = 1.35 atm

V = 1.312 L

T = 371.85 K

And replace in the equation:

PV=nRT

1.35 atm ×1.312 L = n ×0.3821×0.0821 atmL/molK ×371.85K

1.784 atmL= n ×30.53 atmL/mol

n= 0.058 mol

And to find the molecular formula molar mass we have to divide de mol n over the grams given on the excersice 9.91582 g:

9.91582g / 0.082 mol = 170.96 g/mol

And now we can use the formula, and the result has to be approximate to a integer number:

molecular formula molar mass / empirical formula molar mass  = 3.29 = 3

5. Multiply the whole number with the subscripts of the empirical formula:

C3×3H2×3N1×3 = C9H6N3

To see all the problem solve, with the mathematics explained deeply, please watch the document attached.

Molecular formula = C9H6N3