Question #7af06

1 Answer
Mar 29, 2016

Answer:

#"8.4 atm"#

Explanation:

You are right, this is a job for the ideal gas law equation, which as you know looks like this

#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#, where

#P# - the pressure of the gas
#V# - the volume it occupies
#n# - the number of moles of gas
#R# - the universal gas constant, usually given as #0.0821("atm" * "L")/("mol" * "K")#
#T# - the absolute temperature of the gas

Now, every time you're dealing with problems that involve the ideal gas equation, your focus should be on making sure that the units given to you match those used in the expression of the universal gas constant, #R#.

In this particular case, you must convert the volume from milliliters to liters and the temperature from degrees Celsius to Kelvin by using the conversion factors

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 L" = 10^3"mL")color(white)(a/a)|))) " "# and #" "color(purple)(|bar(ul(color(white)(a/a)color(black)(T["K"] = t[""^@"C"] + 273.15)color(white)(a/a)|)))#

So, the problem provides you with #n#, #V#, and #T#, and asks you to find the value of #P#, the pressure of the gas.

What you need to do now is isolate #P# on one side of the ideal gas law equation by dividing both sides by #V#

#(P * color(red)(cancel(color(black)(V))))/color(red)(cancel(color(black)(V))) = (nRT)/V#

#P = (nRT)/V#

Now plug in your values to get the value of #P#

#P = (0.255color(red)(cancel(color(black)("moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * (273.15 + 28)color(red)(cancel(color(black)("K"))))/(748 * 10^(-3)color(red)(cancel(color(black)("L"))))#

#P = "8.429 atm"#

Rounded to two sig figs, the number of sig figs you have for the temperature of the gas, the answer will be

#P = color(green)(|bar(ul(color(white)(a/a)"8.4 atm"color(white)(a/a)|)))#

So, as a conclusion, always check the units first to make sure that they match those used for #R#.

Once you're certain that the units match, isolate whichever variable you must determine on one side of the equation and plug in your values.

As a side note, Dalton's Law of Partial Pressure is applicable for gaseous mixtures, i.e. when you have two or more gases in the same volume.