Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O 2 gas at a pressure of 16,500 kPa at 23 °C. (b) What volume would the gas occupy at STP?

Hey everyone in this example, we're told that a sample of neon gas has the following volume at the pressure, 1.48 E. M. S. And temperature 20 degrees Celsius. We need to determine the volume of the neon sample at standard temperature and pressure. So so far in the prompt, we want to make note of the fact that we're given an initial volume Being equal to 3.60. Leaders were given an initial value for pressure being 1. ATMs And were given an initial value for temperature being 20°C. So we want to recall that we're going to use our gay loose tax law which you recall is taking our initial pressure, multiplying it by the initial volume and dividing it by our initial temperature and setting that equal to our final pressure, multiplied by the final volume and then dividing that by our final temperature. Because we need to solve for our final volume at standard temperature and pressure. We're going to reformat this equation so that we have V two equal to P one times v one times final temperature, T two divided by final pressure and initial temperature. So before we go ahead and fill in our equation here, we want to recall that we're going to use Um temperature values in Kelvin. So we're going to add to 73.152 are given C temperature for the initial temperature and that's going to give us a value in Kelvin of 2 93.15 Kelvin. So plugging in for our equation to solve for final volume. We're going to plug in our initial Pressure given in the prompt as 1.48 e. MS. We're going to multiply this by our initial volume given in the prompt as 3. leaders. And then we're multiplying by our Final temperature which we would assume is going to be standard temperature at 2 73. Kelvin in our denominator. We're going to divide by the final pressure which we would assume at standard pressure conditions is going to be 1 80 M. And then we would multiply this by our initial temperature given in the prompt As 20°C which we converted to Kelvin as to 93 .15 Kelvin and so canceling out our units. We would be able to cancel out kelvin's as well as Our units for pressure 80 M. Leaving us with leaders as our final unit which is what we want for volume and what we're going to get is that our value for the final volume is equal to 4.70 leaders. And this is going to be our final answer to complete this example as the volume of the Neon sample at standard temperature and pressure conditions. So I hope that everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video

Ch.10 - Gases

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Brown 14th Edition

Ch.10 - Gases

Problem 44b

Chapter 10, Problem 44b

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O₂ gas at a pressure of 16,500 kPa at 23 °C. (b) What volume would the gas occupy at STP?

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Identify the initial conditions of the gas: volume \( V_1 = 210.0 \) L, pressure \( P_1 = 16,500 \) kPa, and temperature \( T_1 = 23 \, ^\circ\text{C} \).

Convert the initial temperature from Celsius to Kelvin using the formula \( T(K) = T(\degree C) + 273.15 \).

Recall the conditions for STP (Standard Temperature and Pressure): \( P_2 = 101.3 \) kPa and \( T_2 = 273.15 \) K.

Use the combined gas law \( \frac{P_1 \cdot V_1}{T_1} = \frac{P_2 \cdot V_2}{T_2} \) to solve for the final volume \( V_2 \).

Rearrange the equation to solve for \( V_2 \): \( V_2 = \frac{P_1 \cdot V_1 \cdot T_2}{P_2 \cdot T_1} \).

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Key Concepts

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions and allows for calculations involving changes in state, such as volume at standard temperature and pressure (STP).

Standard Temperature and Pressure (STP)

STP is defined as a temperature of 0 °C (273.15 K) and a pressure of 1 atm (101.3 kPa). At STP, one mole of an ideal gas occupies 22.4 liters. Understanding STP is crucial for converting gas volumes from one set of conditions to another, as it provides a reference point for gas behavior.

Gas Volume Conversion

Gas volume conversion involves using the Ideal Gas Law and STP conditions to determine how the volume of a gas changes with variations in pressure and temperature. This concept is vital for solving problems where the initial and final states of a gas are compared, allowing for the calculation of unknown volumes under specified conditions.

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Common Conversion Factors

Related Practice

Textbook Question

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl₂ gas is 8.70 L at 119.3 kPa and 24 °C. (c) At what temperature will the volume be 15.00 L if the pressure is 116.8 kPa

Textbook Question

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl₂ gas is 8.70 L at 119.3 kPa and 24 °C. (d) At what pressure will the volume equal 5.00 L if the temperature is 58 °C?

Textbook Question

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O₂ gas at a pressure of 16,500 kPa at 23 °C. (a) What mass of O₂ does the tank contain?

Textbook Question

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O₂ gas at a pressure of 16,500 kPa at 23 °C. (c) At what temperature would the pressure in the tank equal 15.2 MPa?

Textbook Question

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O₂ gas at a pressure of 16,500 kPa at 23 °C. (d) What would be the pressure of the gas, in kPa, if it were transferred to a container at 24 °C whose volume is 55.0 L?

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (b) What volume would the gas occupy at STP?

Verified video answer for a similar problem:

Key Concepts

Ideal Gas Law

Standard Temperature and Pressure (STP)

Gas Volume Conversion

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O₂ gas at a pressure of 16,500 kPa at 23 °C. (b) What volume would the gas occupy at STP?