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Multiple Choice
Calculate the temperature in °C of nitrogen gas (N2) with a density of 2.28 kg/m³ at a pressure of 2 atm. (Assume ideal gas behavior and use R = 0.0821 L·atm/mol·K for calculations.)
A
0°C
B
15°C
C
27°C
D
35°C
Verified step by step guidance
1
First, convert the given pressure from atm to the appropriate units for the ideal gas law. Since the ideal gas constant R is given in L·atm/mol·K, we can keep the pressure in atm.
Next, convert the density of nitrogen gas from kg/m³ to g/L. Since 1 kg/m³ is equivalent to 1 g/L, the density is 2.28 g/L.
Use the molar mass of nitrogen gas (N₂), which is approximately 28.02 g/mol, to find the number of moles per liter. This is done by dividing the density by the molar mass: \( \text{moles/L} = \frac{2.28 \text{ g/L}}{28.02 \text{ g/mol}} \).
Apply the ideal gas law in the form \( PV = nRT \), where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Rearrange the equation to solve for T: \( T = \frac{PV}{nR} \).
Substitute the known values into the equation: P = 2 atm, V = 1 L (since we are considering per liter), n = moles/L calculated in step 3, and R = 0.0821 L·atm/mol·K. Solve for T in Kelvin, then convert the temperature from Kelvin to Celsius by subtracting 273.15.