It is possible to verify this idea from multiple sources that are independent of the U.S. Government. I'm going to leave verifying the exact numbers in the question out of scope of this answer, for reasons to be explained shortly, and stick to how you can verify from other sources the underlying claim being taken issue with: that the mass of the liquid is less than the mass of the gas.
Some non U.S. Government sources for this are multiple textbooks on thermodynamics. The combustion of petrochemicals is, understandably, a well-documented process in science and engineering, and there are a lot of sources on this.
I pick An introduction to thermodynamics by Y. V. C. Rao (Universities Press, 2004, ISBN 9788173714610) pretty much at random. Professor Rao teaches chemical engineering at IIT Kanpur in Uttar Pradesh, and seems to have little connection to the U.S. government. In chapter 6 ("First Law Analysis of Processes") we can find several slightly indirect confirmations that this is indeed the physical process:
In combustion process, the mass of each element remains the same even though the reactants disappear and new products are formed. […]
In most of the combustion processes, the required oxygen is not supplied as pure oxygen but is supplied as air. […]
An important parameter in the study of fuels is the air–fuel ratio, the ratio of the mass of the air to the mass of the fuel. […]
One of the more basic ideas that we need to verify can also be found stated by Jeff Hartman, an author on motor vehicles from Austin, Texas. In Nitrous Oxide Performance Handbook (MotorBooks International, 2009, ISBN 9781616730529) on page 24 he says:
When something burns, it is combining with oxygen, i.e. oxidizing.
Rao gives the actual chemical equations for such oxidization, and goes into detail about the purity of the fuel and some generalizations that descriptions of the process tend to make.
For more, we turn to Associate Professor C. Lon Enloe at James Madison University, who tells us on page 13 of Physical Science: What the Technology Professional Needs to Know (John Wiley & Sons, 2001, ISBN 9780471360186) about an important physical principle:
You may know that the conservation of mass and energy (E=mc2) is one of the basic laws of nature. The amount of matter and energy never really change. […] When you burn gasoline, you not only release its chemical energy as heat and light, but you also release matter in the form of carbon dioxide, carbon monoxide, carbon, and water. Every bit of the original matter is conserved.
Let's go to Associate Professor of Mechanical Engineering Gregory Nellis of the University of Wisconsin for another part of the whole. On page 854 of Thermodynamics (Cambridge University Press, 2011, ISBN 9781139498180) he tells us:
The reactants consist of fuel and an oxidizer (usually oxygen). The fuel in a combustion can be gaseous […], liquid (e.g. gasoline or ethane) or solid […].
So what the various professors have told us so far is that there is an underlying physical conservation principle, that there are two inputs (the reactants), and that the mass-energy of the the inputs must equal the mass-energy of the outputs.
But you might challenge this on the principle that carbon dioxide is only one of the outputs, and that the conservation principle is the conservation of mass-energy not of mass alone. Maybe the mass of one of the other products is greater, and thus the mass of carbon dioxide is not necessarily greater than the mass of gasoline that has been burned. Maybe some of the mass turns to energy.
Nellis deals with the latter. This is a chemical reaction, not a nuclear one.
Atoms must be conserved even though the mass of each substance involved in the reaction may change.
This leaves the possibility that the masses of the other products (water, carbon monoxide, and carbon, remember) are such that the mass of carbon dioxide alone is less than the mass of the gasoline. For this, let us turn to Professor of Mechanical Engineering Zellman Warhaft of Cornell University, who gives a more detailed introduction to the process in An Introduction to Thermal-Fluid Engineering: The Engine and the Atmosphere (Cambridge University Press, 1997, ISBN 9780521589277) that shows how the chemical equation that preserves atoms inevitably leads to this result, and that starts off with one of the assumptions that Rao calls out:
Let us assume that C8H8 is representative of gasoline. (In fact, gasoline consists of many different kinds of hydrocarbon molecules, but its average molecular weight is close to that of C8H8.) Equation 1.2 shoes that one molecule of C8H8 produces eight molecules of CO2. Because the molecular weight of C8H8 is 114 and that of CO2 is 44, 1kg of our gasoline produces (8 × 44) ÷ 114 = 3.1 kg of CO2. The density of gasoline is about 70 percent that of water […] and because the density of water is 1000 kg/m3, 1 litre (0.001 m3) of gasoline produces 3.1 × 0.7 = 2.17 kg of CO2, or in the U.S. system 1 gallon (3.785 l) of gasoline produces 18.1 lb of carbon dioxide.
A similar worked example, coming to the figure of 8.196kg of CO2 for 1 gallon of gasoline, is given by Professor Tom Holme of Iowa State University and Senior Lecturer Larry Brown of Texas A&M on page 132 of Chemistry for Engineering Students (Cengage Learning, 2005, ISBN 9780534389741).
Why the discrepancy, though? These are not the U.S. government figure.
The answer lies in the textbooks, again. Internal combustion is complex. There are entire books on this specific subject, after all.
As Rao notes, these explanations make simplifying assumptions. They assume that gasoline is a pure substance. They assume complete combustion. In the real world, gasoline is, as Warhaft says, a mixture. Combustion is not complete. After all, one of the subjects that these textbooks go into is the notion of stoichiometric mass and the ideas of "rich" mixtures where there is too little air and not all of the gasoline burns, and "lean" mixtures where there is too much air. Rao again:
The combustion of a hydrocarbon fuel is considered to be complete if all of the carbon and hydrogen contains in the fuel are converted into carbon dioxide and water, respectively. The minimum amount of air required for the complete combustion of fuel is called the stoichiometric or theoretical air. Usually, the combustion process does not go to completion unless the amount of air supplied is more than the theoretical air. The amount of air actually used in a combustion process is expressed in percent theoretical air or percent excess air. The amount of air supplied over and above the theoretical requirement is called excess air.
And indeed Holme and Brown:
We'll need to know the mass of a gallon of gasoline. As you might guess, this depends on the exact composition of the gasoline in question.
So there is a set of assumptions, about how close one's gasoline is to the theoretical pure octane that the textbook calculations (explicitly) assume, and about how much fuel is actually burned in real automobiles, that can affect the answers. However, the underlying point, that the mass of the carbon dioxide is greater than the mass of the gasoline because mass-energy is conserved, there is another reactant in the reaction, and the chemical equation forces the ratios of reactants to products, is there in these and many other sources.
Interestingly, your skepticism has been studied as one of the things that children do not initially understand about chemistry, and start off with the wrong mental models for. Graham Peacock of Sheffield Hallam University, John Sharp of Bishop Grosseteste University College, Rob Johnsey of the University of Warwick, Debbie Wright of the University of Plymouth, and Keira Sewell of Southampton University noted this in their book Primary Science: Knowledge and Understanding (Learning Matters, 2017, ISBN 9781526422736):
Research into the idea that energy is contained in fuels […] argued that the conservation of matter was one of the most important aspects of understanding energy from fuels and food. The key question was: Suppose we trap all of the fumes from the exhaust pipe of a car and were then able to weigh them — we should be able to compare the amount of petrol used with the amount of exhaust […]. Would the mass of exhaust be:
a. much larger than the petrol?
b. about the same as the mass of the petrol?
c. much smaller than the petrol?
Scientists would answer "a" as the process of burning fuel is constructive because the atoms of the fuel are combined with oxygen. It was found that many people believe (incorrectly) that the amount of exhaust will be smaller than the petrol.
For what they are referring to, which itself cites further works and which again is yet another source for verifying the claim being disputed in the question, see pp. 82 et seq. of Michael Littledyke's, Liz Laikin's, and Keith Ross's book Science Knowledge and the Environment (2000, London: Fulton).
- Richard Stone (2012). "Combustion and fuels". Introduction to Internal Combustion Engines. Palgrave Macmillan. ISBN 9781137028297.
- Kalyan Annamalai and Ishwar K. Puri (2006). Combustion Science and Engineering. CRC Press. ISBN 9780849320712.
- Kenneth W. Ragland, Kenneth M. Bryden (2011). Combustion Engineering. CRC Press. ISBN 9781420092516.
- D. Bradley (2012). "Combustion in Gasoline Engines". In P.M. Weaving. Internal Combustion Engineering: Science & Technology. Springer Science & Business Media. ISBN 9789400907492.
… and so on. Entire books on this subject. ☺