(a) Calculate the density of NO 2 gas at 0.970 atm and 35 °C.

Hey everyone in this example, we have a sample of phosphene gas kept at 8 50 Tour and 35 degrees Celsius. And we need to determine this gasses density. So we're going to use the density form of our ideal gas law where we have our symbol rho for density equal to our pressure of our gas, multiplied by its polarity and then divided by r gas constant R. Times temperature. So from the prompt, we should recognize that we're going to have to convert our pressure from Tour two units of A. T. M. And our temperature from degrees Celsius to kelvin. So starting out with our conversion for pressure, we take the 8 50 tour given from the prompt. And we're going to multiply by the conversion factor to go from Tour to a. T. M. We should recall that for 1 80 M. We have 7 60 tour. So now we're able to cancel out our units for tour, leaving us with a. T. M. As our final unit of pressure. And this gives us our pressure equal to 1.1 to a. T. M's. In the proper units. Now for temperature were given 35 degrees Celsius And we want to go ahead and add to 73.15 Kelvin to convert to Kelvin. And this is going to give us our proper temperature equal to a value of 3.08.15 Kelvin. So now we can go ahead and get into our equation to sulfur density. So what we'll have is that row is equal to in our numerator. We should plug in our pressure, which we converted to 1.1 to a. T. M. This is then multiplied by the molar mass of phosphene. So from our predict table we would see that foss finn has a molar mass equal to a value of 98.91 g per mole. So we're going to plug this in as 91.98 or sorry, .91 g per mole for our Moeller, massive phosphene from the periodic table. And then in our denominator we're going to plug in our ideal gas constant which we should recall a 0.8206 Leaders times a. T. M's divided by moles, times kelvin. This is then going to be multiplied by our temperature which we converted to 308.15 kelvin. And so canceling out our units will be able to get rid of our units of kelvin as well as a T. M. S and also our units of moles. So we're left with grams per leader as our final units, which is what we want for density. And so what we're going to get is a value equal to 4.38 g/s as our final answer to complete this example. So I hope that everything I explained was clear what's boxed in is our final answer for the density of phosphate and gas, if you have any questions just leave them down below and I will see everyone in the next practice video.

Ch.10 - Gases

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Problem 51a

Chapter 10, Problem 51a

(a) Calculate the density of NO₂gas at 0.970 atm and 35 °C.

Verified step by step guidance

Step 1: First, we need to convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is K = °C + 273.15.

Step 2: Next, we will use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. However, we need to rearrange the equation to solve for the density (d) of the gas. The density of a gas is its mass (m) divided by its volume (V), and the mass of a gas is the number of moles (n) times the molar mass (M). So, we can substitute m/V for d and nM for m in the ideal gas law equation to get d = PM/RT.

Step 3: Now, we can plug in the given values into the rearranged ideal gas law equation. The pressure (P) is 0.970 atm, the molar mass (M) of NO2 is 46.01 g/mol (which you can find by adding up the atomic masses of nitrogen and oxygen), the ideal gas constant (R) is 0.0821 L·atm/K·mol (since the pressure is given in atm), and the temperature (T) is the value we calculated in step 1.

Step 4: After plugging in the values, we can solve the equation to find the density of NO2 gas at the given conditions.

Step 5: The final step is to check the units of your answer. The density should be in g/L, which is the mass of the gas divided by the volume it occupies.

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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 calculating properties of gases under various conditions, including density. By rearranging the equation, density can be expressed as d = PM/RT, where d is density, P is pressure, M is molar mass, R is the ideal gas constant, and T is temperature in Kelvin.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For nitrogen dioxide (NO2), the molar mass is calculated by summing the atomic masses of nitrogen (N) and oxygen (O) in the molecule. Understanding molar mass is crucial for converting between mass and moles, which is necessary for applying the Ideal Gas Law to find density.

Gas Density

Gas density is defined as the mass of gas per unit volume, usually expressed in grams per liter (g/L). It can be influenced by factors such as temperature and pressure. In the context of the Ideal Gas Law, density can be calculated using the rearranged formula, allowing for the determination of how much mass of a gas occupies a specific volume under given conditions.

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