The density of a gas at 27^ ^ C and 1 atm pressure is 2.6\ g/dm^3 ....

The ideal gas equation in terms of density is given by $PM = dRT$, where $P$ is pressure, $M$ is molar mass, $d$ is density, $R$ is the universal gas constant, and $T$ is temperature.

Given:
$P = 1 \text{ atm}$
$d = 2.6 \text{ g/dm}^3 = 2.6 \text{ g/L}$
$T = 27^{{}^{\circ}}\text{C} = 27 + 273 = 300 \text{ K}$
$R = 0.0821 \text{ L atm K}^{-1}\text{mol}^{-1}$

Substituting the values into the formula:
$M = \dfrac{dRT}{P}$

$M = \dfrac{2.6 \times 0.0821 \times 300}{1}$

$M = 2.6 \times 24.63 = 64.038 \text{ g/mol}$

Rounding off, we get $M = 64.04 \text{ g/mol}$.

Answer: $64.04$ g/mol