if 3.0 moles of nitrogen gas are collected in a 35.0 liter container at 20 C what would be the the pressure exerted on the container in atmospheres
PV = nRT
where P = pressure, V = volume, R is a constant = 8.314 J/mol*K, and T is temperature in degrees Kelvin, n is number of moles
degrees K = 273 + degrees C
1 liter = 1000 cm^3 = 1000 cm^3* (1 m / 100 cm)^3 = 1000 * (1/1000000) = 1/1000
= 0.001 m^3
35 L = 0.0035 m^3
P*0.0035 = 3*8.314*293
Solve for P
I believe 35.0L is 0.035 m^3; i.e.,
0.001 x 35.0L = 0.0350 m^3
.035
To calculate the pressure exerted on the container, we can use the Ideal Gas Law, which is given by the equation:
PV = nRT
where P represents the pressure, V represents the volume, n represents the number of moles of gas, R is the ideal gas constant, and T represents the temperature in Kelvin.
Given:
Number of moles of nitrogen gas (n) = 3.0 moles
Volume (V) = 35.0 liters
Temperature (T) = 20°C
First, we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature.
T(K) = T(°C) + 273.15
T(K) = 20°C + 273.15
T(K) = 293.15 K
Next, we can substitute the given values into the Ideal Gas Law equation and solve for P:
P * V = n * R * T
Substituting the known values:
P * 35.0 L = 3.0 mol * R * 293.15 K
Now, we need to find the value of the gas constant, R. The ideal gas constant is typically represented by the value 0.0821 L·atm/(mol·K).
Substituting R into the equation:
P * 35.0 L = 3.0 mol * 0.0821 L·atm/(mol·K) * 293.15 K
Simplifying the equation:
P * 35.0 L = 74.0314 L·atm
Finally, we can solve for P by dividing both sides of the equation by 35.0 L:
P = 74.0314 L·atm / 35.0 L
P ≈ 2.115 atm
Therefore, the pressure exerted on the container would be approximately 2.115 atmospheres.