Vapor Density Of Oxygen Calculation Example At STP

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Understanding vapor density is crucial in chemistry, particularly when characterizing gases. Vapor density is the density of a gas relative to hydrogen, providing valuable information about the gas's molecular mass and behavior. This article delves into the calculation of the vapor density of oxygen under standard temperature and pressure (STP) conditions. We'll walk through the necessary steps, formulas, and considerations to accurately determine vapor density, using a practical example involving 0.4 g of oxygen occupying a volume of 0.28 dm³ at STP.

In this exploration of vapor density, it's essential to grasp the fundamental concept: Vapor density is the ratio of the mass of a certain volume of a gas to the mass of the same volume of hydrogen, both measured under the same conditions of temperature and pressure. This dimensionless quantity provides insights into how a gas behaves relative to hydrogen, a standard reference in gas studies. The formula to calculate vapor density is straightforward:

Vapor Density=Molar mass of the gas2\text{Vapor Density} = \frac{\text{Molar mass of the gas}}{2}

This formula stems from Avogadro's law, which states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. Therefore, the vapor density is directly related to the molar mass of the gas. Determining vapor density is significant for several reasons. Firstly, it offers a practical method for approximating the molar mass of a gas, which is essential in stoichiometry and chemical reactions. Secondly, it aids in identifying unknown gases by comparing their vapor densities to known values. Moreover, vapor density plays a crucial role in understanding the physical properties of gases, such as their diffusion rates and behavior in mixtures. Accurately calculating vapor density requires precise measurements of mass, volume, temperature, and pressure, making it a cornerstone technique in experimental chemistry. Understanding vapor density not only enhances our grasp of gas behavior but also underscores its importance in various chemical applications.

To practically illustrate the calculation of vapor density, let’s consider a specific problem: Calculate the vapor density of oxygen, given that 0.4 grams of oxygen occupies a volume of 0.28 dm³ at Standard Temperature and Pressure (STP). Additionally, we are provided with a reference point: the mass of 1000 cm³ of hydrogen at a specific condition (26 j i) is 0.090 g. This reference point will be crucial in our calculations, allowing us to relate the density of oxygen to that of hydrogen. Before diving into the calculations, it's important to clarify the significance of STP conditions. Standard Temperature and Pressure are defined as 0°C (273.15 K) and 1 atmosphere (101.325 kPa). These conditions provide a standard reference for gas measurements, ensuring consistency and comparability across different experiments and calculations. The given data includes:

  • Mass of oxygen: 0.4 g
  • Volume of oxygen: 0.28 dm³
  • Reference data: Mass of 1000 cm³ of hydrogen = 0.090 g

With this information, we can proceed to calculate the vapor density of oxygen. The problem requires us to use the provided hydrogen reference to establish a relative density, which will then lead us to the vapor density. The first step involves converting the given volume of oxygen into a consistent unit, followed by calculating the density of oxygen under STP. Then, we will use the hydrogen reference data to find the density of hydrogen under similar conditions. Finally, we will apply the formula for vapor density to arrive at our result. This step-by-step approach ensures accuracy and clarity in our calculations, providing a robust understanding of the process.

Now, let's embark on a detailed, step-by-step calculation to determine the vapor density of oxygen. This process involves several key stages, each building upon the previous one to ensure accuracy and clarity. We'll start by converting the volume of oxygen to a consistent unit, then calculate the density of oxygen at STP, followed by determining the density of hydrogen using the provided reference data, and finally, apply the vapor density formula. Firstly, we need to ensure all units are consistent. The volume of oxygen is given as 0.28 dm³. Since 1 dm³ is equal to 1000 cm³, we can convert this volume to cubic centimeters:

0.28 dm3=0.28×1000 cm3=280 cm30.28 \text{ dm}^3 = 0.28 \times 1000 \text{ cm}^3 = 280 \text{ cm}^3

Next, we calculate the density of oxygen at STP. Density is defined as mass per unit volume, so:

Density of Oxygen=Mass of OxygenVolume of Oxygen=0.4 g280 cm3≈0.00143 g/cm3\text{Density of Oxygen} = \frac{\text{Mass of Oxygen}}{\text{Volume of Oxygen}} = \frac{0.4 \text{ g}}{280 \text{ cm}^3} \approx 0.00143 \text{ g/cm}^3

Now, we use the reference data for hydrogen. We know that 1000 cm³ of hydrogen has a mass of 0.090 g. Therefore, the density of hydrogen is:

Density of Hydrogen=Mass of HydrogenVolume of Hydrogen=0.090 g1000 cm3=0.00009 g/cm3\text{Density of Hydrogen} = \frac{\text{Mass of Hydrogen}}{\text{Volume of Hydrogen}} = \frac{0.090 \text{ g}}{1000 \text{ cm}^3} = 0.00009 \text{ g/cm}^3

Finally, we can calculate the vapor density of oxygen. Vapor density is the ratio of the density of the gas to the density of hydrogen:

Vapor Density of Oxygen=Density of OxygenDensity of Hydrogen=0.00143 g/cm30.00009 g/cm3≈15.89\text{Vapor Density of Oxygen} = \frac{\text{Density of Oxygen}}{\text{Density of Hydrogen}} = \frac{0.00143 \text{ g/cm}^3}{0.00009 \text{ g/cm}^3} \approx 15.89

Thus, the vapor density of oxygen under the given conditions is approximately 15.89. This step-by-step calculation provides a clear and methodical approach to solving the problem, emphasizing the importance of unit consistency and accurate application of formulas.

To fully grasp the calculation of vapor density, it is essential to delve into the underlying formulas and their significance. The formulas used in this calculation are rooted in fundamental principles of chemistry and gas behavior. Understanding these formulas not only aids in solving similar problems but also enhances the overall comprehension of chemical concepts. The primary formulas we utilized include the density formula and the vapor density formula. The density formula is a cornerstone in physics and chemistry, defined as mass per unit volume:

Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}

This formula is straightforward yet crucial. It allows us to relate the mass of a substance to the space it occupies, providing a measure of how much