You will need to use the ideal gas law to answer this question. The ideal gas law is given by the mathematical formula #"PV"# = #"nRT"#, where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature. When using the gas laws, the temperature needs to be in Kelvins, which is done by adding 273 to the Celsius temperature. The gas constant R can be represented by different units, but in this problem #"R"# = #"0.08206 L atm K"^(−1) "mol"^(−1)"#.
Given/Known:
#"P"# = #"1.000 atm"#
#"V"# = #"100. L"#
#"T"# = #"1325 C"# + #"273"# = #"1598K"#
#"R"# = #"0.08206 L atm K"^(−1)
"mol"^(−1)"#.
Unkown :
number of moles, n
Equation:
#"PV"# = #"nRT"#
Solution:
Divide both sides of the equation by #"RT"# to isolate #"n"#. Solve for #"n"#.
#"n"# = #"PV"/"RT"# = #"(1.000)(100.)""/(0.08206)(1598)"# = #"0.763 mol"# (rounded to three significant figures due to 100. having three significant figures.
Answer:
The number of moles of a gas under the conditions given is #"0.763"#.
