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Answer :
Final answer:
To find the molar mass of the gaseous compound, you can use the ideal gas law equation and the given density and pressure. Convert the given density from g/L to kg/m³ and the given temperature from °C to Kelvin. Then, rearrange the ideal gas law equation and substitute the values to solve for the molar mass.
Explanation:
The molar mass of the compound can be calculated using the ideal gas law and the given density and pressure. First, we need to convert the given density from g/L to kg/m³ by dividing by 1000. Then, we use the ideal gas law equation, PV = nRT, where P is the pressure in Pa, V is the molar volume in m³/mol, n is the number of moles, R is the ideal gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.
First, convert the given pressure from atm to Pa by multiplying by 101325:
P = 1.73 atm × 101325 Pa/atm = 175370.25 Pa
Next, convert the given temperature from °C to Kelvin by adding 273.15:
T = 24.4°C + 273.15 = 297.55 K
Now, rearrange the ideal gas law equation to solve for the molar mass:
molar mass = (P × V) / (n × R × T)
Substitute the given density for the molar mass and solve for n:
n = density × V / molar mass = 1.37 g/L / (molar mass / 1000) = 1.37 kg/m³ / (molar mass / 1000) = (1370 / molar mass) mol/m³
Finally, substitute the values into the rearranged ideal gas law equation and solve for the molar mass:
molar mass = (P × V) / (n × R × T) = (175370.25 Pa × 1 m³/mol) / ((1370 / molar mass) mol/m³ × 8.314 J/mol·K × 297.55 K)
Simplify and solve the equation to find the molar mass of the compound.
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