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the ideal gas
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pV = nRTpressure Volume number of moles Temperature
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pV = nRTFor pV=nRT to work, temperature must be absolute.
For an absolute temperature, T=0 means zero energy.
Kelvin, K is an absolute temperature.
K = oC +273.15
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What is 100 oC in K to the nearest whole number?
What is 100 oC in K to one significant figure?
What is 73 K in oC to the nearest whole number?
What is 73 K in oC to one significant figure?
K = oC +273.15
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pressure is caused by gas molecules hitting the wall of the container.
Volume is size of container.
n is the number of moles ofgas molecules.
R= 8.3 J mol-1 oC-1
Temperature measures the kinetic energy of the gas molecules.
pV = nRT
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p a n
Keeping V and T constant:
if we double n, we double p.
if we triple n, we triple p.
if we halve n, we halve p.
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p a T
Keeping V and n constant:
if we double T, we double p.
if we triple T, we triple p.
if we halve T, we halve p.
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p a V-1
Keeping T and n constant:
if we halve V, we double p.
if we triple V, we reduce pby a third.
if we double V, we halve p.
we say p and V are inversely proportional
n = constant
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p a V-1
p a n
p a T
p a V-1 n TpV a nT
pV = nRT
deducing the ideal gas law based n the previous proportionality relations
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pV = nRTIf we keep T and V constant, if one doubles n what happens to p?
If we keep n and T constant, if one doubles V what happens to p?
If we keep n and p constant, if one doubles T what happens to V?
If we keep p and V constant, if one doubles n what happens to T?
p doubles, n doubles but V stays constant, what happens to T?
p triples, V halves and n doubles, what happens to T?
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proportionality relations
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c = 2p r
c a r p a n
V,T constant
pV = nRTdirectly proportional
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h a w-1
h
h
w
w
Area constant p a V-1
n,T constant
pV = nRTindirectly (inversely) proportional
A = hw
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other proportionality relations exist.
KE = ½ m v2
if velocity doubles, what happens to KE?
if velocity triples, what happens to KE?
if velocity halves, whathappens to KE?
KE is proportional to velocity squared
KE a v2
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if KE quadruples, what happens to v?
if KE doubles, what happens to v?
if KE halves, what happens to v?
KE = ½ m v2
v2 =2 KE _______
m
v = 2 KE _______ m
velocity is proportional to square root of KE.
v a KE
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Where applicable, please state the proportionality relation between the following pairs of quantities. If no proportionality relation exists, please state so. State also, where possible, the proportionality constants.
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V= h x w x dd a wV a w2 x hV a mm is constantV is constanth a 1/w2
Mr. Fantastic
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7.2 (± 0.3) x 109
the digit 7 is the first significant figure.
the exponent is 9.
The most important part of a number is the exponent.
The second most important part of a number is its first significant figure.
The third most important part of a number is the error bar.
0.3 is the error bar.
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sphere
4 p Volume = _____ r3
3
proportion-ality relation is a cubedrelation
proportionailty constantis 4p/3 ≈ 4.
The most important part of a chemistry equation is the proportionality relation.
The second most important part of a chemistry equation is its proportionality constant.
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What are the most important parts of the equations below? Please use the proportionality sign in your answers.
pV = nRT
KE = ½ mv2