Calculate the pressure exerted by a 14.6 mol NH3g in a 3.2 L container at -15.0 celcius using the Van der Waals equation.

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To calculate the pressure exerted by a gas using the Van der Waals equation, we need to use the equation:

P = (nRT) / (V - nb) - a(n/V)^2

Where:
P is the pressure,
n is the number of moles of gas,
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
T is the temperature in Kelvin,
V is the volume of the container,
a and b are constants specific to the gas.

Given:
n = 14.6 mol
R = 0.0821 L·atm/(mol·K)
T = -15.0 °C = 273.15 - 15 = 258.15 K
V = 3.2 L
a = 4.17 L^2·atm/(mol^2)
b = 0.03713 L/mol

Substituting these values into the equation:

P = (14.6 mol * 0.0821 L·atm/(mol·K) * 258.15 K) /
(3.2 L - (0.03713 L/mol * 14.6 mol)) - (4.17 L^2·atm/(mol^2) * (14.6 mol / 3.2 L)^2)

P = (3.77402 L·atm) / (3.2 L - 0.541078 L) - (4.17 L^2·atm/(mol^2) * 6.05885 mol^2/L^2)

P = (3.77402 L·atm) / 2.65892 L - (4.17 L^2·atm/(mol^2) * 36.72655 mol^2/L^2)

P = 1.421 L·atm - 153.213 L·atm/(mol·L)

P = -151.792 L·atm/(mol·L)

Therefore, the pressure exerted by the NH3 gas in the 3.2 L container at -15.0 °C using the Van der Waals equation is approximately -151.792 L·atm/(mol·L).

To calculate the pressure using the Van der Waals equation, we need to substitute the given values into the equation:

\( P = \frac{{RT}}{{V - b}} - \frac{{a}}{{V^2}} \)

where
P = pressure
R = gas constant (ideal gas constant or 0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
V = volume of the container
a = attraction parameter (constant specific to each gas)
b = repulsion parameter (constant specific to each gas)

First, convert the temperature from Celsius to Kelvin:

\( T(K) = T(°C) + 273.15 \)

\( T(K) = -15 + 273.15 = 258.15 K \)

Next, we need the values for the Van der Waals parameters, a and b, for ammonia (NH3). These values can be found in a reference source or given in the problem. For ammonia, the values are approximately:
a = 4.17 atm·L^2/mol^2
b = 0.037 L/mol

Now, plug all the given values into the Van der Waals equation:

\( P = \frac{{RT}}{{V - b}} - \frac{{a}}{{V^2}} \)

\( P = \frac{{0.0821 \ L·atm/(mol·K) \cdot 258.15 \ K}}{{3.2 \ L - 0.037 \ L/mol}} - \frac{{4.17 \ atm·L^2/mol^2}}{{(3.2 \ L)^2}} \)

Simplifying the equation will give you the pressure exerted by the ammonia gas in the container at -15.0 °C.