calculate the percent deviation from ideal behavior: 1.30 mol N2 in a 2.64-L container at 59 °C exerts 27 bar pressure.
To calculate the percent deviation from ideal behavior, we need to compare the pressure exerted by the given gas to the pressure it would exert if it were behaving ideally under the same conditions.
Step 1: Convert the temperature to Kelvin
Given temperature = 59 °C
To convert to Kelvin, add 273.15
Temperature in Kelvin (T) = 59 + 273.15 = 332.15 K
Step 2: Calculate the ideal pressure using the Ideal Gas Law equation
The Ideal Gas Law equation is given by:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.0821 L·atm/(mol·K)), and T is the temperature.
Given:
Number of moles (n) = 1.30 mol
Volume (V) = 2.64 L
Temperature (T) = 332.15 K
Gas constant (R) = 0.0821 L·atm/(mol·K)
Plug in the values into the Ideal Gas Law equation:
P_ideal = (n * R * T) / V
P_ideal = (1.30 mol * 0.0821 L·atm/(mol·K) * 332.15 K) / 2.64 L
Step 3: Calculate the percent deviation from ideal behavior
Percent deviation from ideal behavior = [(P - P_ideal) / P_ideal] * 100
Given:
Pressure (P) = 27 bar
Plug in the values into the percent deviation equation:
Percent deviation from ideal behavior = [(27 bar - P_ideal) / P_ideal] * 100
Now, compute the results using a calculator.
To calculate the percent deviation from ideal behavior, we first need to determine the ideal pressure of the gas using the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K) or 8.314 J/(mol·K) )
T = temperature in Kelvin
Let's convert the given values to the appropriate units:
1. Convert temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 59 + 273.15 = 332.15 K
2. Convert the pressure from bar to atm:
1 bar = 0.98692 atm
P(atm) = 27 bar × 0.98692 atm/bar
P(atm) ≈ 26.64984 atm
Now, we can rearrange the Ideal Gas Law equation to solve for n (number of moles):
n = PV / RT
n = (26.64984 atm) × (2.64 L) / [(0.0821 L·atm/(mol·K)) × (332.15 K)]
n ≈ 1.1349 mol
Now that we have the number of moles, we can calculate the percent deviation from ideal behavior using the following formula:
% Deviation = ((n_ideal - n) / n_ideal) × 100
Where:
n_ideal = number of moles assuming ideal behavior (1.30 mol)
% Deviation = ((1.30 mol - 1.1349 mol) / 1.30 mol) × 100
% Deviation ≈ (0.1651 mol / 1.30 mol) × 100
% Deviation ≈ 12.70%
Therefore, the percent deviation from ideal behavior is approximately 12.70%.
Deviation in what from ideal? Pressure?
P=nRT/V in idkeal, use n, R, T, and V and caculate the predicted pressure. Then
precentdeviation=(P-27bar)/27 * 100