Liquid nitrogen-powered car students at the university of north Texas and the university of Washington built a car propelled by compressed nitrogen gas. The gas was obtained by boiling liquid nitrogen stored in a 185.0 L tank what volume of N2 is released at 0.900 atm or pressure and 25 degrees celcius from a tank full of liquid N2 (d=0.808 g/ml)?
To find the volume of nitrogen gas released, we need to determine the number of moles of nitrogen gas, given the pressure, temperature, and volume of the tank.
First, we need to convert the density of liquid nitrogen from grams per milliliter (g/ml) to grams per liter (g/L). Since there are 1000 milliliters in a liter, the density can be converted as follows:
Density of liquid nitrogen (d) = 0.808 g/ml = 0.808 g/1000 ml = 0.808 g/L
Next, we need to calculate the mass of the liquid nitrogen by multiplying the volume (V) of the tank by the density (d):
Mass of liquid nitrogen (m) = Volume × Density = 185.0 L × 0.808 g/L = 149.78 g
To determine the number of moles (n) of nitrogen gas released, we'll use the ideal gas equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.
We need to convert the given temperature of 25 degrees Celsius to Kelvin:
Kelvin temperature (T) = 273.15 + 25 = 298.15 K
Now we can rearrange the ideal gas equation to solve for the number of moles:
n = PV / RT
Plugging in the given values, we have:
n = (0.900 atm) × (185.0 L) / (0.0821 L·atm/(mol·K) × 298.15 K)
Simplifying, we find:
n ≈ 8.36 moles
Therefore, approximately 8.36 moles of nitrogen gas will be released from the tank.
Note: The volume of nitrogen gas released will depend on the conditions outside the tank (i.e., pressure and temperature). Here, we only calculated the number of moles of gas released.