A glass of cold water contains .45 mM O_2. How many millilitres of oxygen gas at STP are dissolved in 300.0 mL of this water?

1 Answer
Nov 30, 2015

Answer:

There will be 3.1 mL of oxygen gas dissolved in 300 mL of solution.

Explanation:

Convert mM to M.

#0.45cancel"mM O"_2""xx(1"M O"_2"")/(1000cancel"mM O"_2"")="0.00045 M O"_2"#

#"0.00045 M O"_2"##=##"0.00045 mol/L O"_2"#

Convert 300 mL to liters.

#300.0cancel"mL solution"xx(1"L")/(1000cancel"mL")="0.3000 L solution"#

Determine moles of #"O"_2"# dissolved in #"0.3000 L"# of solution.

#0.3000cancel"L solution"xx(0.00045"mol O"_2)/(1cancel"L solution")="0.000135 mol O"_2"#

#"STP"="273.15 K" and "100 kPa"#

Use the Ideal Gas Law

#PV=nRT#, where #P="pressure"#, #V="volume"#, #n="moles"#, #R="gas constant"#, and #T="Kelvin temperature"#.

Given/Known
#P="100 kPa"#
#n="0.000135 mol O"_2"#
#R="8.3144598 L kPa K"^(-1) "mol"^(-1)"#
#T="273.15 K"#

Unknown
volume, #V#

Solution
Rearrange the equation to isolate #V# and solve.

#V=(nRT)/P#

#V=(0.000135cancel"mol O"_2xx8.3144598"L" cancel("kPa") cancel("K"^(-1)) cancel("mol"^(-1))xx273.15cancel"K")/(100cancel"kPa")="0.00307 L O"_2"#

Convert liters to milliliters.

#0.00307cancel"L O"_2xx(1000"mL")/(1cancel"L")="3.1 mL O"_2"# (rounded to two significant figures)