We're doing gas problems in chemsitry. I have no idea where to even begin on this problem:

Air is 20% oxygen and 80% nitrogen. What is the mass of air in an automobile tire of 19.7 L and internal pressure of 46.7 PSI at 24 degrees celsius? (That pressure is the same as the 32 PSI difference you usually measure as the tire pressure 32 PSI + 14.7 PSI. You will have to use a weighted average for the molar mass of air.)

First the weighted average for the molar mass of air.

(0.8 x molar mass N2) +(0.2 x molar mass O2) = about 28.8 but you can do that more accurately.

Next the pressure of the tire in psi. We need that in atmospheres. I went to google and typed in 46.7 psi to atm and it returned 3.178 atm.

Now use PV = nRT
You know P, you know V from the problem, you know R (0.08206) and you know T (24 C + 273 = ??K). Calculate n = number of moles air.

Then moles = grams/molar mass. yOu know moles (n) and you know molar mass air (about 28.8 g/mol), calculate grams. That's your answer.

Oh, chemistry and gas problems. They always leave us gasping for air, don't they? Well, fear not! Clown Bot is here to help you navigate through this comedic chaos.

To solve this problem, we'll need to break it down into smaller steps. Let's get started!

First, let's find the molar mass of air using a weighted average. Take a look at the periodic table and find the molar masses of oxygen (O) and nitrogen (N). Oxygen has a molar mass of approximately 16 grams per mole, while nitrogen is around 14 grams per mole.

Now, let's calculate the weighted average. Since air is 20% oxygen and 80% nitrogen, we can multiply the molar mass of each element by their respective percentages and then add them together. It's weighing time!

(0.2 * 16) + (0.8 * 14) = ?

Hey, wait a minute! You don't improve the molar mass by adding some pounds to it!

The correct calculation is: (0.2 * 16) + (0.8 * 14) = 15.2 grams per mole

Okay, now that we have the molar mass, let's move on to the mass of air in the tire. We can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

But, since we're all about mass here, we can modify the equation a bit to solve for mass instead. Instead of n, let's use m/M, where m is the mass and M is the molar mass.

P * V = (m/M) * R * T

Let's rearrange it to solve for m:

m = (P * V * M) / (R * T)

Now, plug in the values:

P = 46.7 PSI + 14.7 PSI = 61.4 PSI (converted from PSI to atm, of course!)

V = 19.7 L

M = 15.2 g/mol (the molar mass that we calculated earlier)

R = 0.0821 atm L/mol K (the gas constant)

T = 24 + 273.15 = 297.15 K (converted from Celsius to Kelvin)

Now, all that's left is to put the numbers in and find the mass:

m = (61.4 * 19.7 * 15.2) / (0.0821 * 297.15) = ?

Calculating, calculating... and drumroll, please!

m ≈ 410.75 grams

Ta-da! The mass of air in the automobile tire (at least according to my calculations) is around 410.75 grams.

Now that we've solved this problem, we can finally let out a sigh of relief... or should I say air of relief? Keep up the great work, and don't hesitate to ask if you need any more help!

To solve this problem, you will need to use the ideal gas law and the concept of partial pressures.

The ideal gas law is expressed as follows:
PV = nRT

Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)

Let's break down the steps to solve the problem:

Step 1: Convert the given pressure to atmospheres.
To convert from PSI to atmospheres, divide the pressure by 14.7 PSI/1 atmosphere.

46.7 PSI / 14.7 PSI/1 atm = 3.17 atm

Step 2: Convert the given temperature from Celsius to Kelvin.
To convert from Celsius to Kelvin, add 273.15 to the temperature.

24 °C + 273.15 = 297.15 K

Step 3: Determine the mole fraction of oxygen and nitrogen in the air.
The mole fraction of oxygen is given as 20%, which means 0.20 moles of oxygen for every 1 mole of air. The mole fraction of nitrogen is 80%, which means 0.80 moles of nitrogen for every 1 mole of air.

Step 4: Calculate the moles of oxygen and nitrogen.
Since you have the mole fractions, you can assume 1 mole of air for calculation convenience. Therefore, the moles of oxygen and nitrogen would be equal to their respective mole fractions.

moles of oxygen = 0.20
moles of nitrogen = 0.80

Step 5: Calculate the total moles of air in the tire.
The total moles of air can be calculated by adding the moles of oxygen and nitrogen.

Total moles of air = moles of oxygen + moles of nitrogen

Step 6: Calculate the mass of air in the tire.
To calculate the mass of air, you need the molar mass of air. Since air is a mixture of oxygen and nitrogen, you will need to use a weighted average.

The molar mass of oxygen (O2) is approximately 32 g/mol, and the molar mass of nitrogen (N2) is approximately 28 g/mol.

molar mass of air = (moles of oxygen * molar mass of oxygen) + (moles of nitrogen * molar mass of nitrogen)

Step 7: Use the ideal gas law to calculate the moles of air.
Rearranging the ideal gas law equation, we can solve for moles of air (n):

n = PV / RT

where P is the pressure in atmospheres, V is the volume in liters, R is the ideal gas constant, and T is the temperature in Kelvin.

Step 8: Calculate the mass of air.
Finally, multiply the total moles of air by the molar mass of air to find the mass of air.

mass of air = moles of air * molar mass of air

Following these steps will help you solve the problem and find the mass of air in the automobile tire.

To solve this problem, we need to calculate the mass of air in the automobile tire. We can do this by following a step-by-step process:

Step 1: Convert the given pressure from PSI to atm
The conversion factor between PSI and atm is 1 atm = 14.7 PSI. Therefore, the internal pressure of the tire in atm is 46.7 PSI + 14.7 PSI = 61.4 PSI (approximately).

Step 2: Convert the given volume from liters to moles
To convert the volume of the tire from liters to moles, we need to use the ideal gas law equation: PV = nRT. Rearranging the equation, we have n = PV / RT, where P is the pressure, V is the volume, R is the gas constant, and T is the temperature. The gas constant R is 0.0821 L·atm/(K·mol).
Substituting the values:
n = (61.4 PSI) * (19.7 L) / (0.0821 L·atm/(K·mol) * (24 °C + 273.15 K)
Note: We converted °C to Kelvin by adding 273.15.

Step 3: Calculate the mole fraction of oxygen and nitrogen
Since air consists of 20% oxygen and 80% nitrogen, we can determine the mole fractions of each component.
Mole fraction of oxygen = 20% = 0.2
Mole fraction of nitrogen = 80% = 0.8

Step 4: Calculate the average molar mass of air
To find the average molar mass of air, we can use the weighted average method. The molar mass of oxygen (O2) is approximately 32 g/mol, while the molar mass of nitrogen (N2) is approximately 28 g/mol.
Average molar mass of air = (mole fraction of oxygen * molar mass of oxygen) + (mole fraction of nitrogen * molar mass of nitrogen)

Step 5: Convert moles to grams
Finally, we can calculate the mass of air in the tire by multiplying the number of moles of air (calculated in Step 2) by the average molar mass of air (calculated in Step 4). The result will be the mass of air in grams.

By following these steps, you should be able to arrive at the solution.