Final answer:
The question asks for the pressure of an ideal gas in a pipe given its temperature, density, and molar mass. We use the ideal gas law with appropriate unit conversions (temperature to Kelvin, density to g/L) to calculate the pressure in kilopascals.
Step-by-step explanation:
The student's question is seeking the pressure of an ideal gas flowing in a pipe at a specific temperature, density, and known molar mass. To solve this, we can use the ideal gas law, which is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.
To find the pressure (P), we first need to convert the temperature to Kelvin by adding 273.15 to the Celsius temperature: T = 37°C + 273.15 = 310.15 K. We can find the number of moles (n) by dividing the density (ρ) by the molar mass (M), ρ/M. The molar mass given is 44 kg/kmol, which is equivalent to 44 g/mol as 1 kmol = 1000 mol. We can now calculate the number of moles in 1 cubic meter (m³) as n = 2.1 kg/m³ ÷ 44 kg/kmol.
The ideal gas constant (R) is 8.314 kPa·L/(mol·K) when pressure is in kilopascals. To apply the ideal gas law correctly, we must ensure all units are compatible. Therefore, we also need to convert the density from kg/m³ to g/L which is a simple transformation given that 1000 g = 1 kg and 1000 L = 1 m³.
Putting these values into the ideal gas equation and solving for P gives us the pressure of the gas in the pipe. We can then compare our calculated result with the answer choices provided.