Empirical/molecular formula problems using the ideal gas law and density of a gas
Cyclopropane, a gas once used with oxygen as a general anesthetic, is composed of 85.7% carbon and 14.3% hydrogen by mass. Find the empirical formula. If 1.56 g of cyclopropane occupies a volume of 1.00 L at 0.984 atm and 50 °C, what is the molecular formula for cyclopropane?
Solution
Strategy: First solve the empirical formula problem using methods discussed earlier. Assume 100 g and convert the percentage of each element into grams. Determine the number of moles of carbon and hydrogen in the 100-g sample of cyclopropane. Divide by the smallest number of moles to relate the number of moles of carbon to the number of moles of hydrogen. In the last step, realize that the smallest whole number ratio is the empirical formula:
Empirical formula is CH
2 [empirical mass (EM) of 14.03 g/empirical unit].
Next, use the density equation related to the ideal gas law to determine the molar mass:
ℳ = 42.0 g/mol,
so (3)(CH
2 ) = C
3 H
6 (molecular formula)
Check your learning
Acetylene, a fuel used welding torches, is comprised of 92.3% C and 7.7% H by mass. Find the empirical formula. If 1.10 g of acetylene occupies of volume of 1.00 L at 1.15 atm and 59.5 °C, what is the molecular formula for acetylene?
Another useful application of the ideal gas law involves the determination of molar mass. By definition, the molar mass of a substance is the ratio of its mass in grams,
m , to its amount in moles,
n :
The ideal gas equation can be rearranged to isolate
n :
and then combined with the molar mass equation to yield:
This equation can be used to derive the molar mass of a gas from measurements of its pressure, volume, temperature, and mass.
Determining the molar mass of a volatile liquid
The approximate molar mass of a volatile liquid can be determined by:
Heating a sample of the liquid in a flask with a tiny hole at the top, which converts the liquid into gas that may escape through the hole
Removing the flask from heat at the instant when the last bit of liquid becomes gas, at which time the flask will be filled with only gaseous sample at ambient pressure
Sealing the flask and permitting the gaseous sample to condense to liquid, and then weighing the flask to determine the sample’s mass (see
[link] )
When the volatile liquid in the flask is heated past its boiling point, it becomes gas and drives air out of the flask. At
the flask is filled with volatile liquid gas at the same pressure as the atmosphere. If the flask is then cooled to room temperature, the gas condenses and the mass of the gas that filled the flask, and is now liquid, can be measured. (credit: modification of work by Mark Ott)
Using this procedure, a sample of chloroform gas weighing 0.494 g is collected in a flask with a volume of 129 cm
3 at 99.6 °C when the atmospheric pressure is 742.1 mm Hg. What is the approximate molar mass of chloroform?
Solution
Since
and
substituting and rearranging gives
then
Check your learning
A sample of phosphorus that weighs 3.243
10
−2 g exerts a pressure of 31.89 kPa in a 56.0-mL bulb at 550 °C. What are the molar mass and molecular formula of phosphorus vapor?
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
