the ideal gas

pV = nRTpressure Volume number of moles Temperature

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

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

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

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.

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.

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

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

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?

proportionality relations

c = 2p r

c a r p a n

V,T constant

pV = nRTdirectly proportional

h a w-1

h

h

w

w

Area constant p a V-1

n,T constant

pV = nRTindirectly (inversely) proportional

A = hw

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

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

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.

V= h x w x dd a wV a w2 x hV a mm is constantV is constanth a 1/w2

Mr. Fantastic

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.

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.

What are the most important parts of the equations below? Please use the proportionality sign in your answers.

pV = nRT

KE = ½ mv2