Answer:
295.4K
Step-by-step explanation:
Step 1:
Obtaining an expression which relates density, pressure and temperature together.
This is can done by using the ideal gas equation as shown below:
PV = nRT........... (1)
Recall:
Number of mole (n) = mass (m) /Molar Mass (M) i.e
n = m/M
Substituting the m/M for n in equation 1 above
PV = nRT
PV = mRT/M
Divide both side by P
V = mRT/MP
Divide both side by m
V/m = RT/MP
Invert the above equation
m/V = MP/RT.....(2)
Density (D) = mass (m) /volume (V)
D = m/V
Replacing m/V with D in equation 2.
m/V = MP/RT
D = MP/RT
Step 2:
Data obtained from the question. This includes the following:
Density (D) = 2.22 g/L
Pressure (P) = 1.04 atm
Molar Mass of (M) = 51.7 g/mol.
Temperature (T) =.?
Gas constant (R) = 0.082atm.L/Kmol
Step 3:
Determination of the temperature.
D = MP/RT
2.22 = 51.7 x 1.04 / 0.082 x T
Cross multiply to express in linear form
2.22 x 0.082 x T = 51.7 x 1.04
Divide both side by 2.22 x 0.082
T = (51.7 x 1.04) /(2.22 x 0.082)
T = 295.4K
Therefore, the temperature of the gas is 295.4K