Find the number of moles in 2.00L of gas at 35 degree Celsius and under 74100000N/m square.
To calculate the number of moles of gas, we need to use the ideal gas law:
PV = nRT
Where:
P = pressure = 74100000 N/m^2
V = volume = 2.00 L
n = number of moles (what we're solving for)
R = gas constant = 8.31 J/(mol K) (we need to convert from Nm/(mol K) to J/(mol K))
T = temperature = 35 + 273 = 308 K (we need to convert from Celsius to Kelvin)
So, first, let's convert the gas constant:
R = 8.31 J/(mol K) / 1000 Nm/(mol K) = 0.00831 m^3 N/(mol K)
Now we can plug in the values:
74100000 N/m^2 * 2.00 L = n * 0.00831 m^3 N/(mol K) * 308 K
Simplifying:
n = (74100000 N/m^2 * 2.00 L) / (0.00831 m^3 N/(mol K) * 308 K)
n = 16.9 mol
So there are approximately 16.9 moles of gas in 2.00L at 35 degrees Celsius and under 74100000 N/m^2.
To find the number of moles of gas, you need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in Pascals)
V = volume (in cubic meters)
n = number of moles
R = gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given values to the appropriate units:
Pressure: 74100000 N/m²
Volume: 2.00 L (convert to m³)
Temperature: 35 °C (convert to K)
1 L = 0.001 m³ (conversion factor)
Temperature in Kelvin = 35 + 273.15
Now we can calculate the number of moles:
P = 74100000 N/m²
V = 2.00 L * 0.001 m³/L = 0.002 m³
R = 8.314 J/(mol·K)
T = 35 °C + 273.15 = 308.15 K
Plug in the values into the ideal gas law equation:
PV = nRT
74100000 N/m² * 0.002 m³ = n * 8.314 J/(mol·K) * 308.15 K
Simplifying the equation:
148200 N = n * 2560.589 J/(mol)
Solving for n (number of moles):
n = 148200 N / 2560.589 J/(mol)
n ≈ 57.77 mol
Therefore, there are approximately 57.77 moles of gas in 2.00 L at 35 °C and under a pressure of 74100000 N/m².