In: Chemistry

Use the ideal gas law to complete the table:

P |
V |
n |
T |

1.06 atm | 1.25 L | 0.105 mol | ___ |

115 torr | ___ | 0.249 mol | 309 K |

___ | 28.2 mL | 1.81×10^{−3} mol |
26.0 ∘C |

0.565 atm | 0.440 L | ___ | 257 K |

For an ideal gas, consider the molar volume Vm = (V/n) =
Vm(T,P). In other words, the molar volume is a function of
temperature and pressure.
a) Write the total differential dVm.
b) Show that dVm is exact.
c) Derive an expression for the differential work dw performed
in a reversible process by expansion/compression of the gas.
d) Show that dw is inexact.
e) What is the thermodynamic significance of having an exact
differential?

The ideal gas law can be stated as P V = nRT where P = pressure
in Pascals (Pa) V = volume in cubic meters (m3 ) n = number of
moles in moles (mol) R = gas constant = 8.3145m3 Pa / ( K · mol ) T
= temperature in Kelvin (K). Using MATLAB or Octave, Write a script
that prompts the user for the pressure, the volume, and the
temperature; storing each in a variable. The script...

The ideal gas law PV=nRT relates pressure P, volume V,
temperature T, and number of moles of a gas, n. The gas constant R
equals 0.08206 L⋅atm/(K⋅mol) or 8.3145 J/(K⋅mol). The equation can
be rearranged as follows to solve for n: n=PVRT This equation is
useful when dealing with gaseous reactions because stoichiometric
calculations involve mole ratios.
Part A
When heated, calcium carbonate decomposes to yield calcium oxide
and carbon dioxide gas via the reaction CaCO3(s)→CaO(s)+CO2(g) What
is the mass...

Suppose 1.0 mol of an ideal gas is initially at P=4.0
atm and T=400 K. It is expanded irreversibly and adiabatically
against a constant pressure of 1.0 atm until the volume has
doubled.
(a) Calculate the final volume of the gas.
(b) Calculate w, q, and energy change ΔU of this process, in
joules.
(c) Calculate the final temperature of the gas.
(d) Calculate the entropy change ΔS of the ideal gas in the
process.
(e) What is the entropy...

For 1 mol of an ideal gas, Pexternal = P = 1 atm. The
temperature is changed from 125ºC to 25.0ºC, and CV,m = 3/2R.
Calculate (all units are J) q= , w= , ∆U= , and ∆H= . Please enter
your answers with 2 decimals in E notation, such as 2.33E4
(=23345). If the answer is negative, please do not forget the
negative sign. If answer is zero, please just enter 0 without
decimal.

Use Charles's law to complete the table. (Assume pressure and
number of moles of gas to be constant.)
Part
V1
T1
V2
T2
A
119 L
10.2 ∘C
__
106.4 ∘C
B
__
135 K
173 L
314 K
C
2.15 L
16.4 ∘C
2.23 L
__
D
15.6 cm3
__
18.2 cm3
10.1 ∘C
A&B Express the volume in liters to three significant
figures.
C&D Express the temperature in degrees Celsius to three
significant figures.

One mole of an ideal gas in an initial state P = 10atm, V = 5L,
is taken reversibly in aclockwise direction around a circular path
given by (V − 10)^2 + (P − 10)^2 = 25. Computethe amount of work
done by the gas and the change in internal energy.

Two moles of an ideal gas originally at T = 400 K and
V = 40 L undergo a free expansion;
?2 = 10?1
. Find (a) the entropy change of the gas, and (b) the entropy
change of the universe?

1 Ideal Gas Law The ideal gas law is familiar to anyone who has
taken a college chemistry course: P V = νRT. This problem will show
you why the ideal gas law has this form. We can arrive at this
expression just by using classical mechanics! Consider a box of
volume V containing N particles, each having mass m, that are
moving horizontally with average speed v. The particles bounce back
and forth between the end walls of the...

Calculus dictates that
(∂U/∂V) T,Ni = T(∂S/∂V)T,Ni – p = T(∂p/∂T)V,Ni – p
(a) Calculate (∂U/∂V) T,N for an ideal gas [ for which p = nRT/V
]
(b) Calculate (∂U/∂V) T,N for a van der Waals gas
[ for which p = nRT/(V–nb) – a (n/V)2 ]
(c) Give a physical explanation for the difference between the
two.
(Note: Since the mole number n is just the particle number N
divided by Avogadro’s number, holding one constant is equivalent...

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