Question #25bda

1 Answer
Jun 4, 2017

Answer:

(c) #257# #"kg"#

Explanation:

We're asked to find the mass of #"O"_2# in a #1000# #"L"# tank at #27# #""^"o""C"# with an internal pressure of #2.0 xx 10^7# #"Pa"#.

Every time you're given three of the four basic characteristics of a gas (pressure, volume, temperature, and/or moles), you'll be using the ideal-gas equation:

#PV = nRT#

where

  • #P# is the pressure of the gas, expressed in atmospheres (#"atm"#).

Since the pressure in this case is given in pascals, we have to convert this to atmospheres, using the conversion factor

#1# #"atm" = 101,325# #"Pa"#

#2.0 xx 10^7# #cancel("Pa")((1"atm")/(101,325cancel("Pa"))) = color(red)(197# #color(red)("atm"#

  • #V# is the volume occupied by the gas, expressed in liters, which is given as #color(orange)(1000)# #color(orange)("L")#

  • #n# is the quantity of gas present, in moles, which is what we must find in order to calculate the mass of oxygen present

  • #R# is called the universal gas constant, and is equal to #color(purple)(0.08206 ("L · atm")/("mol · K")#

  • #T# is the absolute temperature of the system, "absolute" indicating that the temperature is in units of Kelvin, #"K"#

Since our given temperature is in degrees Celsius, we have to convert this to Kelvin using the formula

#"K" = ""^"o""C" + 273#

#"K" = 27^"o""C" + 273 = color(green)(300)# #color(green)("K")#

Now that we have all our necessary units, let's use the ideal-gas equation to find the number of moles of #"O"_2# present, by rearranging the equation to solve for #n#:

#PV = nRT#

#n = (PV)/(RT)#

#n = ((197cancel("atm"))(1000cancel("L")))/((0.08206 (cancel("L") "·" cancel("atm"))/("mol" "·" cancel("K")))(300cancel("K"))) = 8018# #"mol O"_2#

Now that we know the moles of gas present, we can use the molar mass of #"O"_2#, #32.00"g"/"mol"#, to calculate the number of grams of oxygen:

#8018# #cancel("mol O"_2)((32.00"g O"_2)/(1cancel("mol O"_2))) = 2.566 xx 10^5# #"g O"_2#

Lastly, let's convert this to kilograms:

#2.566 xx 10^5# #cancel("g O"_2)((1"kg O"_2)/(10^3cancel("g O"_2))) = color(blue)(257# #color(blue)("kg O"_2#

Thus, the correct answer is (c).