26.0 g/mol
The ideal gas law is
PV = nRT
where
P = pressure
V = volume
n = amount of substance
R = ideal gas constant (8.3144598 (L kPa)/(K mol) )
T = absolute temperature
Solving for n, gives
PV = nRT
PV/RT = n
Convert pressure from mmHg to kPa
752 mmHg = 752 * 0.133322387415 = 100.2584353 kPa
Convert temperature from C to K
25.0 C = 25.0 C + 273.15 = 298.15 K
Volume will be 1 liter.
Substitute known values into equation solving n
PV/RT = n
(100.2584353 kPa * 1 L)/(8.3144598 (L kPa)/(K mol) 298.15 K) = n
(100.2584353 kPa L)/(2478.956189 (L kPa)/mol) = n
0.040443811 mol = n
So we know we have 0.040443811 moles of the unknown gas.
Now just divide the mass of the gas by the number of moles.
1.053 g / 0.040443811 mol = 26.03612214 g/mol
Rounding to 3 significant figures give 26.0 g/mol
