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calculate the molar mass of a gas if 3.30 grams of the has occupies 660 ml at 735mmHg and 27 degrees C

Verified Answer :

mrbrowntown956

Use the ideal gas law PV = nRT and manipulate it to solve for n. PV/RT = n.
Convert to SI units:
660ml -> 0.660 L
27 degrees -> 300 K
Leave Pressure as is
Use 62.36368 for R becuase you are using mmHg for Pressure.
Now plug into the equation to get about 0.025928 mols. Divide the 3.30 grams by the mols to get about 127 g/mol.

onyebuchinnaji

The molar mass of the gas that occupies the given volume is 127.4 g/mol.

The given parameters;

  • mass of the gas, m = 3.3 g
  • volume of the gas, V = 660 ml = 0.66l
  • pressure of the gas, P = 735 mmHg
  • temperature of the gas, T = 27 ⁰C = 273 + 27 = 300 K

The number of moles of the gas is calculated form ideal gas law as follows;

PV = nRT

where;

  • n is the number of moles
  • R is the gas constant = 62.36 L.mmHg/mol.K

\(n = \frac{PV}{RT} \\\ = \frac{0.66 \times 735}{62.36 \times 300} \\\ = 0.0259 \ mole\)

The molar mass of the gas is calculated as follows;

\(no. \ mole = \frac{reacting \ mass}{molar \ mass} \\\\molar \ mass = \frac{reacting \ mass}{no.\ mole} \\\\molar \ mass =\frac{3.3}{0.0259} \\\\molar \ mass = 127.4 \ g/mol\)

Thus, the molar mass of the gas that occupies the given volume is 127.4 g/mol.

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