Chapter 5 Lecture Problems

A cylinder with a movable piston has a volume of 7.25 L at 4.52 atm. What is the volume at 1.21 atm?

V1 =7.25 L, P1 = 4.52 atm, P2 = 1.21 atm, V2= ?P1 · V1 = P2 · V2

V1, P1, P2 V2

V2 = =(P1)(V1)!(P2)

(4.52 atm)(7.25 L)!(1.21 atm)

= 27.1 L

V2 =2780 mL, P1 = 762 torr, P2 = 0.500 atm V1 = ?

V2, P1, P2 V1

P1 · V1 = P2 · V2 , 1 atm = 760 torr (exactly) !

A balloon is put in a bell jar and the pressure is reduced from !782 torr to 0.500 atm. If the volume of the balloon is now !

2.78 x 103 mL, what was it originally?

D = m/V

A balloon is put in a bell jar and the pressure is reduced from !782 torr to 0.500 atm. If the volume of the balloon is now !

2.78 x 103 mL, what was it originally?

A gas has a volume of 2.57 L at 0.00 °C. What was the temperature when the volume was 2.80 L?

V2 =2.57 L, T2 = 0.00 °C, V1 = 2.80 L T1 = ?

V1, V2, T2 T1

(2.80 L)(2.57 L)

The temperature inside a balloon is raised from 25.0 °C !to 250.0 °C. If the volume of cold air was 10.0 L, what is the

volume of hot air?

V1 =10.0 L, t1 = 25.0 °C L, t2 = 250.0 °C V2 = ?

V1, T1, T2 V2

V2 = =(T2)(V1)!(T1)

= 17.5 L(523.2 K)(10.0 L)!(298.2 K)

V1!T1

V2!T2

=T(K) = t(ºC) + 273.15

T1 = 25.0 + 273.15 = 298.2 KT2 = 250.0 + 273.15 = 523.2 K

If 1.00 mole of a gas occupies 22.4 L and the temperature and pressure are not changed, what volume would !

0.750 moles occupy?

V1 =22.4 L, n1 = 1.00 mol, n2 = 0.750 mol V2 = ?

V1, n1, n2 V2

V1!n1

V2!n2

=

(V1)(n2)!(n1)

V2 = = 16.8 L(22.4 L)(0.750 mol)!(1.00 mol)=

A gas occupies 10.0 L at 44.1 psi and 27 °C. What volume will it occupy at standard conditions?

V1 = 10.0L, P1 = 44.1 psi, t1 = 27 °C, P2 = 1.00 atm, t2 = 0 °C, V2 = ?

P1, V1, T1, R n

n = PV!RT V = nRT!

P

P2, n, T2, R V2

1.00 atm!14.7 psi

44.1 psi x = 3.00 atm

T1(K) = 27ºC + 273.15 = 300. K

n = PV!RT

= 1.218 mol

atm L!mol K

(3.00 atm)(10.0 L)!(0.0821 )(300. K)=

= 1.22 mol

A gas occupies 10.0 L at 44.1 psi and 27 °C. What volume will it occupy at standard conditions?

n =1.218 mol

P1, V1, T1, R n

n = PV!RT V = nRT!

P

P2, n, T2, R V2

V = (1.22 mol)(.0821 )(273 K)!1.00 atm

atm L!mol K

= 27.3 L

Calculate the volume occupied by 637 g of SO2 (MM 64.07) at 6.08 x 104 mmHg and –23 °C.

mSO2 = 637 g, P = 6.08 x 104 mmHg, t = −23 °C, V = ?

g n P, n, T, R V

K = 273+ºC=273+(-23)=250

How many liters of O2 @ STP can be made from the decomposition of 100.0 g of PbO2?

2 PbO2 → 2 PbO + O2

100.0 g PbO2, PbO2: 239.2 g/mol, O2: 32.00 g/mol, L O2 = ?

g PbO2 mol O2mol PbO2 L O2

g

mol

mol

mol

mol

L

100.0 g PbO2 x x x 1.0 mol PbO2!239.2 g PbO2

1.0 mol O2!2.0 mol PbO2

22.4 L O2!1.0 mol O2

= 4.68 L O2

Calculate the density of N2(g) at STP.

molar!mass density g!

L

d = = = 1.25 molar mass g/mol!molar volume L/mol

28.02 g/mol!22.4 L/mol

g!L

Calculate the density of N2 at 125°C and 755 mmHg .

P = 755 mmHg, t = 125 °C, dN2 = ?

P, MM, T, R d

Calculate the density of a gas at 775 torr and 27 °C if 0.250 moles weighs 9.988 g.

m = 9.988 g, n = 0.250 mol, P = 775 torr, T = 27ºC, density = ?

K = 273+ºC=273+(27)=300

P, n, T, R V V, m d

V = (n)(R)(T)!P

d = m!V

(0.250 mol)(0.0821 )(300 K)!(1.02 atm)

atm L!mol K

775 torr x = 1.0197 atm 1 atm!760 torr

V = = !! ! ! ! ! = 6.037 L

(n)(R)(T)!P

Calculate the density of a gas at 775 torr and 27 °C if 0.250 moles weighs 9.988 g.

m = 9.988g, n = 0.250 mol, P = 775 torr, T = 27ºC, density = ?

V, m d P, n, T, R V

V = (n)(R)(T)!P

V = 6.037 L

V = (n)(R)(T)!P

d = 9.988 g!6.037 L

= 1.65 g/L

Calculate the molar mass of a gas with mass 0.311 g that has a volume of 0.225 L at 55°C and 886 mmHg.

m=0.311g, V=0.225 L, P=886 mmHg, T = 55 ºC, molar mass(MM) = ?

P, V, T, R n

n = (P)(V)!(R)(T)

K = 273+ºC=273+(55)=328

n, m MM

MM = m!n

886 mmHg x = 1.1658 atm 1 atm!760 mmHg

n = = (P)(V)!(R)(T)

(1.17 atm)(0.225 L)!(0.0821 )(328 K)atm L!

mol K

= 9.7754 x10-3 mol

Calculate the molar mass of a gas with mass 0.311 g that has a volume of 0.225 L at 55°C and 886 mmHg.

m=0.311g, V=0.225 L, P=886 mmHg, T = 55 ºC, molar mass = ?

n = 9.7754 x10-3 mol

n = (P)(V)!(R)(T)

P, V, T, R n

n = (P)(V)!(R)(T)

MM = 0.311 g!9.78 x 10-3 mol

n, m MM

MM = m!nMM = m!n

MM = 31.8 g/mol

What is the molar mass of a gas if 12.0 g occupies 197 L at 3.80 x 102 torr and 127 °C?

m=12.0 g, V= 197 L, P=380 torr, t=127°C, molar mass = ?

P, V, T, R n n, m MM

K = 273+ºC=273+(127)=400

Find the partial pressure of neon in a mixture of neon and xenon with total pressure 3.9 atm, volume 8.7 L,

temperature 598 K, and 0.17 moles Xe.

Ptot = 3.9 atm, V = 8.7 L, T = 598 K, Xe = 0.17 mol , PNe = ?

nXe, V, T, R PXe Ptot, PXe PNe

Find the mole fractions and partial pressures in a 12.5 L tank with 24.2 g He and 4.32 g O2 at 298 K.

mHe = 24.2 g, mO2 = 4.32 g, V = 12.5 L, T = 298 K!!χHe, χO2, PHe, PO2, Ptotal = ?????

mgas ngas χgas

χgas, Ptotal Pgas

ntot, V, T, R Ptot

1.02 L of O2 collected over water at 293 K with a total pressure of 755.2 mmHg. Find the mass of O2.

V=1.02 L, P=755.2 mmHg, T=293 K, mass O2 = ?

Ptot, PH2O PO2 PO2,V,T nO2 gO2

0.12 moles of H2 is collected over water in a 10.0 L container at 323 K. Find the total pressure in torr.

V=10.0 L, nH2 = 0.12 mol, T = 323 K, Ptotal = ?

nH2,V,T PH2 PH2, PH2O Ptotal

What volume of H2 is needed to make 37.5 g of CH3OH at 738 mmHg and 355 K?

CO(g) + 2 H2(g) → CH3OH(g)

mCH3OH = 37.5g, P=738 mmHg, T=355 K , VH2 = ?

g CH3OH mol CH3OH mol H2 P, n, T, R V

How many grams of H2O form when 1.24 L H2 reacts completely with O2 at STP?O2(g) + 2 H2(g) → 2 H2O(g)

VH2 = 1.24 L, P = 1.00 atm, T = 273 K massH2O = ?

g H2O L H2 mol H2 mol H2O

What volume of O2 at 0.750 atm and 313 K is generated by the thermolysis of 10.0 g of HgO?2 HgO(s) → 2 Hg(l) + O2(g)

(MMHgO = 216.59 g/mol)

mHgO = 10.0g, P=0.750 atm, T=313 K VO2 = ?

g HgO mol HgO mol O2 P, n, T, R V

Calculate the rms velocity of O2 at 25 °C

MM, T urms

√3RT MMurms=

Calculate the ratio of rate of effusion for oxygen to hydrogen.

O2, 32.00 g/mol; H2 2.016 g/mol = ?

This means that, on average, the O2 molecules are traveling at ¼ the speed of H2 molecules.

0.251

Calculate the molar mass of a gas that effuses at a rate 0.462 times N2.

MMgas A = ?

rateA/rateB, MMN2 MMunknown

MMN2 = 28.02 g/mol