Considering the ideal gas law PV=nRT, what is P directly proportional to what variable?

Question

Natalie Anton · Accepted Answer

Pressure is directly proportional to temperature and number of moles.

This is how the ideal gas law equation appears. #PV = nRT#, where #P# - the pressure of the gas; #V# - its volume; #n# - the number of moles of gas; #R# - the gas constant, usually given as #0.082("atm" * "L")/("mol" * "K")# #T# - the temperature of the gas. Two variables need to increase or decrease at the same rate in order to have a direct relationship. Put differently, two variables are directly proportional if, when one is increased, the other is also increased at the same rate; conversely, if one is decreased, the other is also decreased at the same rate. To see which variables are directly proportional to pressure, isolate #P# on one side of the equation #(P * color(red)(cancel(color(black)(V))))/color(red)(cancel(color(black)(V))) = (nRT)/V# #P = (nRT)/V# Since #R# is a constant, you can say that #P# is proportional to #P prop (nT)/V# So, #P# is directly proportional to the product between #n# and #T# and inversely proportional to #V#. In other words, if #n# increases while #T# and #V# remain unchanged, then #P# will increase as well. Likewise, if #T# increases while #n# and #V# remain constant, the #P# will Increase as well. On the other hand, if #n# and #T# are unchanged, then any increase in #V# will cause #P# to decrease. As a conclusion, #P# is directly proportional to #n# and #T# and inversely proportional to #V#.

Naomi Aronson · Answer

undefined P is directly proportional to T (temperature).