Large amounts of nitrogen gas are used in the manufacture of ammonia, principally for use in fertilizers. Suppose 120.00 kg of N 2 (g) is stored in a 1100.0-L metal cylinder at 280 °C. (b) By using the data in Table 10.3, calculate the pressure of the gas according to the van der Waals equation.

Hi everyone for this problem, we're being asked to calculate the pressure in a 500 liter industrial tank containing 322.4 kg of oxygen at 25°C using the Vander Wal's equation. Okay, so we want to calculate pressure and the Vander wal's equation is P is equal to N R T Over V -9B minus a times and squared over V squared. Okay, So P is our pressure and his moles are is our gas constant. T is our temperature, V is volume. And is our moles again, B is our Vander wal's constant for gas molecules. So is A and is our moles as we said, and V is our volume. So let's go ahead and write out what we know, solve for what we don't know and then plug this all into our equation. So the first thing that we need to know is N. N. is our moles. So the problem tells us that we have 322 0.4 kg of oxygen. We need to convert this kilograms of oxygen two moles of oxygen and we can do that by using the molar mass of oxygen. However molar masses in grams. So we need to convert this kilograms two g. So in one kg we have 1000 g. Okay, so now our units of kilograms cancel and we need to go from grams of 022 moles of 02. And we can do that using molar mass. So one mole of 02. So we have two oxygen's here. And so the mass of two oxygen's is 32 g of oxygen. Okay, so our grams of oxygen cancel and we're left with moles of oxygen. So let's solve for that. And when we do we get N. Is equal to 10, malls Of 0. 2. Okay, so we have our n. Alright, our is our universal gas constant. This is something that we should know. It is 0. leaders times atmosphere over more times kelvin R. T. is temperature because our gas constant has the unit for temperature in Kelvin. We're told in the problem that our temperature is 25°C. So we need to convert this to Kelvin by adding 273.15. When we do that, we get a temperature in kelvin Of 298.15 Calvin. Okay, we said V is our volume. They tell us we have a 5000 leader industrial tank. Our unit leader here is perfect. We don't need to convert anything so we can leave that as is so for our Vander wal's constants for gas molecules, we need to look up the values for A and B. So our gas is oxygen gas. And when we refer to the the table Or look up the value, the B constant for oxygen gas is 0. 3184 leaders Permal And are a constant is equal to 1.36 leader squared times A. T. M over mole squared. Okay, so these are all of our values for the units and our Van der Waals equation. So now what we can do is plug it all in and solve for pressure. Okay, so let's go ahead and do that. So our pressure is going to equal N R T. So let's do that first. So we get 10, 75 moles times are 0. leaders times A. T. M over times Calvin times T To 98.15 Kelvin. This is all over v minus N. B. So we have 505,000 leaders minus and times be So we have our N is our moles 10,075. Malls times are be constant, Which is zero leaders over. Okay, and this is going to be minus A. R.A. 1.36. Leader square times A T. M. Over more squared. So this is minus eight times N squared over V squared. So our moles squared 10075. Most of Yeah, so this is moles squared over. So don't forget to square that 10,075 over our volume squared. So 5000 leaders squared. Okay, so once we plug all of that in to our calculator, we're going to get a final answer of 4:47. A T. M. Okay, and this is going to be our final answer for this problem. This is the pressure that's going to be in this industrial tank using the Vander Waals equation. That's the end of this problem. I hope this was helpful.

Ch.10 - Gases

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Brown 15th Edition

Ch.10 - Gases

Problem 109b

Chapter 10, Problem 109b

Large amounts of nitrogen gas are used in the manufacture of ammonia, principally for use in fertilizers. Suppose 120.00 kg of N₂(g) is stored in a 1100.0-L metal cylinder at 280 °C. (b) By using the data in Table 10.3, calculate the pressure of the gas according to the van der Waals equation.

Verified step by step guidance

Identify the van der Waals equation: \( \left( P + \frac{an^2}{V^2} \right) (V - nb) = nRT \), where \( a \) and \( b \) are van der Waals constants for nitrogen.

Convert the mass of nitrogen gas to moles using its molar mass: \( n = \frac{\text{mass}}{\text{molar mass}} \).

Convert the temperature from Celsius to Kelvin: \( T(K) = T(°C) + 273.15 \).

Substitute the values for \( n \), \( V \), \( T \), and the van der Waals constants \( a \) and \( b \) for nitrogen into the van der Waals equation.

Solve the van der Waals equation for pressure \( P \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Van der Waals Equation

The Van der Waals equation is an adjustment of the ideal gas law that accounts for the volume occupied by gas molecules and the attractive forces between them. It is expressed as (P + a(n/V)²)(V - nb) = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and a and b are constants specific to each gas. This equation is particularly useful for real gases under high pressure and low temperature conditions.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. While it provides a good approximation for many gases, it does not account for intermolecular forces or the volume of gas particles, which is where the Van der Waals equation becomes relevant.

Gas Properties and Conditions

Understanding the properties of gases, including pressure, volume, temperature, and the number of moles, is crucial for solving gas-related problems. Pressure is the force exerted by gas molecules colliding with the walls of their container, while volume is the space the gas occupies. Temperature affects the kinetic energy of gas molecules, influencing their behavior. These properties are interrelated and can be manipulated using equations like the Ideal Gas Law and Van der Waals equation to predict gas behavior under various conditions.