Estimating Total Air Molecules in a Room | Help with Homework Statement

  • Thread starter Teenytiny1991
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    Estimation
In summary, to estimate the total number of air molecules in a room with dimensions of 20ft x 14ft x 8ft, we can use the conversion factors 1 mole = 22.4 liters and 6.02 x 10^23 molecules = 1 mole. By converting the volume of the room to liters and using the conversion factors, we can calculate the total number of air molecules in the room.
  • #1
Teenytiny1991
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Homework Statement



Estimate to 1 significant figure the total # of air molecules in this room (l=20ft, w=14ft, H= 8ft) Find molecules/room

Homework Equations


1 mole = 22.4 liters
6.02 x 10^23 molecules = 1 mole


The Attempt at a Solution



volume of room = 2240 ft^3 or approx 683 m^3

6.02x10^23 Molecules / 1 mole x 1 mole/ 22.41 liters = 6.02 x10^23 molecules/ 22.41 liters... I am stuck here. how do i figure out how many liters are in the room?
 
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  • #2
Welcome to PF!

Hi Teenytiny1991! Welcome to PF! :smile:

(oooh, you're even smaller than i am! :biggrin:)
Teenytiny1991 said:
… volume of room = 2240 ft^3 or approx 683 m^3

how do i figure out how many liters are in the room?

(try using the X2 tag just above the Reply box :wink:)

How many cm3 to a litre?

How many cm to a foot? :smile:
 
  • #3


I would approach this problem by first converting the given dimensions of the room from feet to meters, as the volume of the room is typically measured in cubic meters. This can be done by using the conversion factor 1 ft = 0.3048 m.

So, the length (l) of the room would be 20 ft x 0.3048 m/ft = 6.096 m, the width (w) would be 14 ft x 0.3048 m/ft = 4.2672 m, and the height (H) would be 8 ft x 0.3048 m/ft = 2.4384 m.

Next, I would calculate the volume of the room by multiplying the three dimensions together: 6.096 m x 4.2672 m x 2.4384 m = 62.8 m^3.

Now, using the given conversion factor of 1 mole = 22.4 liters, I would convert the volume of the room from cubic meters to liters: 62.8 m^3 x 1000 liters/m^3 = 62,800 liters.

Finally, I would use the Avogadro's number (6.02 x 10^23 molecules/mol) to calculate the total number of air molecules in the room: 6.02 x 10^23 molecules/mol x 62,800 liters/22.4 liters/mol = 1.7 x 10^27 molecules.

Therefore, the estimated total number of air molecules in the room is approximately 1.7 x 10^27 molecules. It is important to note that this is only an estimate, as the actual number may vary due to factors such as temperature, pressure, and humidity in the room.
 

1. What is an estimation problem?

An estimation problem is a mathematical or statistical problem where the goal is to find a reasonable approximation of a certain value or quantity. This is often done using available data and mathematical models.

2. How is an estimation problem different from a prediction problem?

While both estimation and prediction involve making educated guesses or approximations, an estimation problem typically focuses on finding a single value or quantity, while a prediction problem involves forecasting future values or outcomes.

3. What are some common techniques used to solve an estimation problem?

Some common techniques used to solve estimation problems include statistical methods like regression analysis and hypothesis testing, as well as mathematical methods like calculus and optimization.

4. What types of data are typically used in an estimation problem?

Data used in estimation problems can vary, but often includes numerical data such as measurements, counts, or percentages. It can also include categorical data, such as demographic information, that can be used to classify and analyze the numerical data.

5. What are some real-world examples of estimation problems?

Estimation problems can be found in various fields such as finance, economics, engineering, and social sciences. Some examples include estimating the population size of a city, predicting the stock market trends, or determining the best production level for a manufacturing company.

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