Answer :
Answer:
The density of this gas is 1.079 g/L
Explanation:
Step 1: Data given
Temperature of the gas = 59.1 °C = 273.15 + 59.1 = 332.25 Kelvin
Pressure of the gas = 1.05 atm
Molar mass of the gas = 28.01 g/mol
Step 2: Calculate density
Density ρ = mass / volume
p*V = n*R*T
⇒ with p = the pressure of the gas = 1.05 atm
⇒with V= the volume of the gas = unknown
⇒ with n = the number of moles
⇒ with R = the gas constant = 0.08206 L*atm/K*mol
⇒ with T = the temperature of the gas = 332.25 Kelvin
Since we don't know the number of moles, either the volume; we will calculate n/v
n/V =P/RT
Since ρ = m/V
and mass m = moles n * Molar mass MM
We can say that: (P*MM)/RT = (n*MM)/v = m/V = ρ
so ρ = (P*MM)/RT
ρ = (1.05 atm*28.01g/mol) / (0.08206 L*atm/K*mol *332.25 Kelvin)
ρ = 1.079 g/L
The density of this gas is 1.079 g/L
Final answer:
The density of the unknown gas, calculated using the ideal gas law and given values is approximately 1.15 kg/m³.
Explanation:
Let's calculate the density of the gas using the ideal gas law and the given values. The ideal gas law is expressed as PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Given the molar mass of 28.01 g/mol, pressure of 1.05 atm, and temperature of 59.1 °C (which we need to convert to Kelvin by adding 273.15), we can find the gas's density, which is mass/volume.
First, let's convert all the units to standard units: P=1.05atm=1.05x101325Pa=105342.25Pa, T=59.1C=59.1+273.15=332.25K. Combining these into density formula (Density (p) = MP/RT), we get:
Density (p) = (28.01 g/mol) (105342.25Pa) / ((8.314 J/K.mol) (332.25K))
Performing the calculation results in a density of about 1.15 kg/m³. So, the density of the unknown gas is approximately 1.15 kg/m³.
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