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Not being a native speaker of English, one of those words that tripped me up is “cocoa”. Besides having its vowels inverted from “cacao”; it also is pronounced exactly the same as “coco”, whereas “cacao” isn't pronounced “caca” and “boa” isn't pronounced “bo”. So why is the “a” in “cocoa” silent?

Phonetic spelling from a dictionary:

cocoa |ˈkōkō|
noun

1 a chocolate powder ...

coco |ˈkōkō|
noun ( pl. -cos)

1 [usu. as adj. ] coconut : coco matting ...

cacao |kəˈkou; kəˈkāō|
noun ( pl. -os)

1 beanlike seeds from which cocoa ...

boa |ˈbōə|
noun

1 a constrictor snake ...

A few sources indicate it's due to initial confusion between coco, cocoa, and cocao.

According to Dictionary.com, the confusion started circa 1545 when cocao was misspelled as cocoa.

But, according to the Online Eytmology Dictionary, the pronunciation issue occurred with the 1707 printing of Johnson's Dictionary that ran coco next to cocoa, stirring confusion between the two words.

Following up on user2512's answer, I quote Online Etymology Dictionary's entry for cocoa in full:

cocoa (n.) powder from cacao seeds, 1707, corruption (by influence of coco) of cacao. The printing of Johnson's dictionary ran together the entries for coco and cocoa, fostering a confusion that never has been undone.

Samuel Johnson, A Dictionary of the English Language, volume 1, (1756), however, doesn't have an entry for coco (or coconut) at all, though it does have one for chocolate and another for cocoa:

CHOCOLATE. s. {chocolate, Span.} 1. The nut of the cocao-tree 2. The mass made by grinding the kernel of the cocao-nut, to be dissolved in hot water. 3. The liquor made by a solution of chocolate. Arbuthnot, Pope.

...

COCOA. s. {cacaotal, Spanish} A species of palm-tree. The bark of the nut is made into cordage, and the shell into drinking bowls. The kernel of the nut affords wholesome food, and the milk contained in the shell a cooling liquor. The leaves of the trees are used for thatching houses. This tree flowers twice or three times in the year, and ripens as many series of fruits. Miller, Hill.

These entries strongly suggest two things. First, Johnson was well aware of the difference between what he called cocao (the source of chocolate) and what he called cocoa (the source of coconuts). Johnson's entry for chocolate mentions both the "cocao-tree" and the "cocao-nut," and his entry for cocoa describes in some detail the characteristics and virtues of the coconut palm. Second, it is misleading to say that Johnson's dictionary "ran together the entries for coco and cocoa." Rather, it adopted the spelling cocoa for the coconut palm and omitted any entry for what Johnson had earlier identified as "the cocao-tree."

Forty years before Johnson, Elisha Coles, An English Dictionary (1717) has entries for chocolate and coco:

Chocolate, an Indian drink made of Cocao.

...

Coco, an Indian Tree, of the rind whereof is made Cordage for Ships, &c.

Noteworthy here is that Coles is already using cocao instead of cacao as the spelling for the nut that produces chocolate.

But the more surprising thing about Johnson's spelling cocoa for the coconut palm is that he had translated a book in 1735 that especially noted the coconut palm and had spelled the word coco there. From Johnson's 1735 translation of Jerome Lobo, A Voyage to Abyssinia (by 1660):

The vessels most used in the Red sea, though ships of all sizes may be met with there, are gelves, of which some mention hath been made already ; these are the more convenient, because they will not split if thrown upon banks, or against rocks. These gelves have given occasion to the report, that out of the coco tree alone a ship may be built, fitted out with mast, sails, and cordage ; and victualled with bread, water, wine, sugar, vinegar and oil. ... There is not a month in which the coco does not produce a bunch of nuts, from twenty to fifty.

Moreover, Johnson did some additional research into aspects of Abyssinia that were mentioned in Lobo's account, which he published as "A Dissertation on the Eastern Side of Africa, from Melinda to the Streight of Babelmandel" (1735), and which contained the following remarks about "cocos":

The author [Lobo] hath said so much already of the usefulness of the palm, that I shall not enlarge upon what has been written by him, but shall content myself with saying something of the coco of the Maldives, and the tree which produces it. ... When the coco is ripe, it separates from the tree, and is carried by the waves to each shore, where the inhabitants heap them up, and sell them, as an excellent antidote, at a large price.

Nevertheless, in later editions of Johnson's works, editors changed coco to cocoa.

A Google Books search for coco, cacao, cocao, and cocoa reveals that the first three words were mentioned multiple times in English texts by the end of the seventeenth century; cocoa, however, although it appears in the end 1690s, seems to have been the last of the four spellings to emerge.

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coco

From Thomas Herbert, Some Yeares Travels Into Divers Parts of Asia and Afrique (1638):

The Coco (an excellent fruit) is cover'd with a thick rynd; both together, Coco. equall in bignesse to a Cabbage: the shell is like the skull of man, or rather a Deaths head; eyes, nose and mouth, being easily discerned; intus vita! within we find better than the out-side promised; a quart of Ambrosie, coloured like new white Wine, but farre more aromatick tasted; the meat or kernell cleaves to the shell, and is not easily parted; above an inch thick, better relisht than our Philberts, and enough to satiate the appetite of two reasonable men.

The shape of which [namely, of a palmetto tree] and Coco, after my rude way I thus present thee: Their excellencies I cannot more elegantly expresse, than Silvester has already celebrated.

The Indian I'les most admirable be/In those rare fruits call'd Coquo's commonly:/...

From Robert Boyle, Some Considerations Touching the Usefulnesse of Experimental Naturall Philosophy, second edition (1664):

And in the East Indies, Linschoten tels us of a change much more suddain : For speaking of the formerly mention'd Sura or Liquor, afforded by the wounded Coco tree. The same water (says he) standing but one Houre in the Sunne is very good Vinegar, and in India they have none other.

And from Robert Hooke, Micrographia: Or, Some Physiological Descriptions of Minute Bodies Made by Magnifying Glasses with Observations and Inquiries thereupon (1667):

There are a multitude of other seeds which in shape represent or imitate the forms of divers other sorts of Shells: as the seed of Scurvy-grass, very much resembles the make of a Concha Venerea, a kind of Purcelane Shell ; others represent several sorts of larger fruits, sweet Marjerome and Pot-marjerome represent Olives. Carrot seeds are like a cleft of a Coco-Nut Husk ; others are like Artificial things, as Succory seeds are like a Quiver full of Arrows, the seeds of Amaranthus are of an exceeding lovely shape, somewhat like an Eye : The skin of the black and shriveled seeds of Onyons and Leeks are all over knobbed like a Seals skin.

The words coco and coco-nut continued to appear frequently throughout the eighteenth century.

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cacao

From a translation of the account of Cortez's expedition in Mexico by Bernaldus del Castillo, in Henry Stubbs, The Indian Nectar, Or a Discourse Concerning Chocolata: Wherein the Nature of the Cacao-nut, and the other Ingredients of that Composition, is examined, and stated according to the Judgment and Experience of the Indians, and Spanish Writers, who lived in the Indies, and others ; with sundry additional Observations made in England: ... (1662):

They brought in the several sorts of fruits, which they had in their Country, but they eat but a very little of them, and that but leisurely, and at intervals : they brought some in cups of fine gold, with a certain drink made of the Cacao it self, which they said was effectual to provoke lustful desires towards women (as they told us in their language) in which we admired nothing more, then that they brought in above fifty great jarrs made of good Cacao, with its froth, and that they drank it, the women serving them with a great deal of respect : and when he {Motezuma} did eat, several Indians stood by him, which gave thanks, and others, which sung to him, and danced before him, Motezuma being much given to pleasure : and he commanded the reliques of his feast be given away, and the jarrs of Cacao.

From Thomas Gage, A New Survey of the West-Indies: Or the English American his Travel by Sea and Land (1677):

But lastly to conclude with this Indian drink [chocolate], I will add what I have heard Physicians of the India's say of it, and have seen it by experience in others (though never I could find it in my self) that those that use this Chocolatte much, grow fat and corpulent by it : which indeed may seem hard to believe ; for considering that all the ingredients, except the Cacao, do rather extenuate, then make fat, because they are hot and dry in the third degree. And we have already said, that the qualities which do predominate in Cacao, are cold and dry, which are very unfit to add any substance to the body. Nevertheless it may be answered that the many unctuous parts, which have been proved to be in the Cacao, are those which pinguefie and make fat ; ...

And from William Dampier, A New Voyage Round the World: Describing Particularly, The Isthmus of America, Several Coasts and Islands in the West Indies, the Isles of Cape Verd, ... volume 1 (1699):

But the main Product of these Valleys [along the Coast of Caraccos], and indeed the only Commodity it vends, are the Cacao-Nuts, of which the Chocolate is made. The Cacao-Tree grows no where in the North Seas but in the Bay of Campeachy, on Costa Rica, between Portabel and Nicaragua, chiefly up Carpenters River ; and on this Coast as high as the Isle of Trinidada. ... Besides these, I am confident, there's no places in the World where the Cacao grows, except those in Jamaica, of which there are now but few remaining, of many and large Walks or Plantations of them found there by the English at their first arrival, and since planted by them ; ...

This book is also interesting in that it includes a variant spelling Cacoa in the chapter table of contents for chapter 3, where the preceding excerpt appears:

The Coast of Caraccus, its remarkable Land, and Product of the best Cacoa Nuts. The Cacao described at large withe Husbandry of it. ...

Like coco, cacao appears in English books throughout the eighteenth century as well.

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cocao

From An Alphabetical Table of the Philosophical Transactions [of the Royal Society] from March 6, 1665, to July 1677 (1677):

The Cocao and Chocolato tree ; the way of its curing and husbandry, &c. n. 93, p. 6007

The reference, however, is to the April 21, 1673, number of Philosophical Transactions, where the spelling is Cacao throughout:

An accurate description of the Cacao-tree, and the way of its Curing and Husbandry, &c., given by an Intelligent person now residing in Jamaica.

From "An Act for Granting to Their Majesties certain Additional Impositions upon several Goods and Merchandize for the Prosecuting the present War against France" in Anno Regni Gulielmi Et Mariae, Regis & Reginae Angliae (1692):

And for every Hundred Weight of Cocao Nuts Imported, and containing, as aforesaid, Eight Pounds, and Eight Shillings over and besides what was then paid for the same at the Custom House : And for every Pound Weight of Tea Imported Five Shillings : And for every Pound Weight of Chocolate ready made Five Shillings over and besides what was then Charged on Tea or Chocolate respectively at the Custom House, which Duties are so excessive that few of the said Goods or Merchandizes have been Entred at the Custom House since the Making of the said Act, or any Duty answered to Their Majesties for the same.

From William Salmon, The Family Dictionary: Or, Houshold Companion, fourth edition (1710):

For Chocolet, see Cocao Nut, Lett. C. No. 167

...

167. 
     Cocao Nut : Nux Cacao of which Chocolet is made. It grows in the West-Indies, where they call it Cacavate. There are several kinds of the Nut, distinguished by the Provinces or Places where it grows. The best Nuts are the Caracca Nuts ; those which grow in Martineco, and other Islands, are nothing near so good, but have a bitter Taste with them.

And from The Natural History of Chocolate: Being a Distinct and Particular Account of the Cocao-Tree, Its Growth and Culture, and the Preparation, Excellent Properties, and Medicinal Vertues of Its Fruit (1724), pages 2 and 6:

The Cocao-Tree is moderately tall and thick, and either thrives, or not, according to the Quality of the Soil wherein it grows: Upon the Coast of Caraqua, for instance, it grows considerably larger than in the Islands belonging to the French.

...

The Fruit of the Cocao-Tree is contained in a Husk or Shell, which from an exceeding small Beginning, attains, in the space of four months, to the Bigness and Shape of a Cucumber; the lower End is sharp and furrow'd length-ways like a Melon (c).

But note this contrary identification of a "Cocao Tree" in John Smith, The True Travels, Adventures, and Observations of Captain John Smith, from Ann. Dom. 1593 to 1629 (1630):

This Kingdom [Congo] is divided into five Provinces, viz., Bamba, Sundi, Pango, Batta, and Pembo; but Bamba is the Principal, and can afford 400000 Men of War. Elephants are bred over all those Provinces, and of wonderful greatness; though some report, they cannot kneel, nor lie down, they can do both, and have their Joynts as other Creatures for use: With their Fore-feet they will leap upon Trees to pull down the Boughs, and are of that strength., they will shake a great Cocao Tree for the Nuts, and pull down a good Tree with their Tusks, to get the leaves to eat, as well as Sedge and long Grass, Cocao Nuts and Berries, &c., which with their Trunk they put in their Mouth, and chew it with their smaller Teeth; ...

Since their were no cacao trees in Africa in the late 1500s and early 1600s, it seems probable that Smith is talking about coconut palms here. Similarly, in a letter of February 16, 1702, from Father Tanchard, Superiour-General of the French Missionary-Jesuits, in the East-Indies, to Father De la Chaize reproduced in Travels of the Jesuits, into Various Parts of the World, second edition (1762), the author describes the experiences of three shipwrecked Englishmen struggling to survive on a small island northwest of Madagascar:

These unfortunate Persons were graciously received by the King of the Western Part of the Island [of Angasia] where they landed. He first entertained them at his own Expence ; but soon growing weary of this Hospitality, he left them to provide for themselves as they could. During a Year and a half they subsisted upon the Fruit of the Cocao, and the Milk of Cows they met with straggling ; after which, one of them being unable to live any longer in that manner, fell sick and died.

Like the Congo in 1630, the Comoro Islands in 1717 are exceedingly unlikely to have had cacao trees. It is far likelier that the travelers were subsisting on coconuts.

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cocoa

Among the earliest Google Books matches for the spelling cocoa appear in connection with a coffee—or rather chocolate—shop called The Cocoa Tree. The first mention of it occurs in the first issue of The Spectator, in a name-dropping allusion that suggests it was already rather well known in London. From Joseph Addison, The Spectator (March 1, 1711):

Sometimes I smoke a pipe at Child's ; and whilst I seem attentive to nothing but the Postman, overhear the conversation of every table in the room. I appear on Sunday nights at St. James's coffee-house, and sometimes join the little committee of politics in the inner room, as one who comes there to hear and improve. My face is likewise very well known at the Grecian, the Cocoa-Tree, and in the theatres both of Drury-Lane and Hay-Market.

From Humphrey Broadbent, The Domestick Coffee-Man, Shewing the True Way of Preparing and Making of Chocolate, Coffee and Tea (1722), page 1:

Cocoa Nuts, whereof Chocolate is made, grow in the West-Indies, and their goodness is according to the place they come from.

The best are the Caracca-Nuts ; those which grow in the Martinico, and other, Islands, are nothing near so good, but have a bitter Taste in them, they grow in Husks about the bigness of an Almond, and almost like one, being of a brown Colour.

From Esdras Barnivelt [actually, Alexander Pope], "A Key to the Lock: Or, A Treatise Proving, Beyond All Contradiction, the Dangerous Tendency of a Late Poem, Entituled, The Rape of the Lock, to Government and Religion" (1723):

Upon the Day that this Poem was published, it was my Fortune to step into the Cocoa Tree, where a certain Gentleman was railing very liberally at the Author, with a Passion extremely well counterfeited, for having (as he said) reflected upon him in the Character of Sir Plume. Upon his going out, I enquired who he was, and they told me, a Roman Catholick knight.

Survey of London: The Parish of Westminster: South of Piccadilly (1960) [combined snippets] dates the opening of the Cocoa Tree Club to no later than 1698:

No. 64 St. James's Street: Weltje's and the Cocoa Tree Club

The first known reference to the Cocoa Tree chocolate house is in 1698. During its long career it occupied three different houses in Pall Mall and then moved to No. 64 St. James's Street. At some unknown date it ceased to be a place of public resort and became first a proprietary and then (probably) a members' club. When it ceased to exist in 1932 it was, apart from White's, the only West End club whose ancestry could be traced back to the chocolate houses of the late seventeenth century.

From "Exchequer, and Exchequer-Bills," in An Exact Abridgment of All the Statutes in Force and Use from Magna Charta, volume 2 (1725):

CVIII, And that the Bank may be enabled to circulate the said bills, by exchanging them for Ready Money on Demand, the yearly Sum of 8000*l.* shall be paid to them ... to commence on the 31 of July 1713, ... and that the Duties 7 A. viz. the two Thirds of a Subsidy of Tonnage and Poundage, the Duties on Coffee, Cocoa-Nuts, Chocolate, Cocoa-Paste, Tea, Nutmegs, Cinnamon^ Cloves, Mace, and Pictures, White Callicoes, China Ware, and Drugs, &c. shall be a Fund to satisfy the same.

The same book cites similar statutes in the "Excise" chapter, again with the spellings Cocoa-Nuts and Cocoa-Paste, dated May 1, 1701, and June 23, 1710, respectively. Indeed the one dated May 1, 1701, was an existing law set to expire on that date but instead continued for six more years.

So far we've seen only early instances that use the spelling cocoa to refer to the cacao plant or its seeds. But one very early writer consistently uses cocoa to refer to coconut palms. From Thomas Phillips, A Journal of a Voyage Made in the Hannibal of London, Ann. 1693, 1694, from England, to Cape Monseradoe, in Africa, and thence along the Coast of Guiney to Whidaw, the Island of St. Thomas, and so forward to Barbadoes (1694):

Near the cod of the bay [at St. Jago in the Cape Verde Islands] is a very large cocoa-nut orchard, with plenty of fruit, in which near the sea-side is a large hole, where they told me there us'd to be fresh water to supply shipping; ...

A drawing on the preceding page of the book confirms that the "cocoa-nut orchard" consists of coconut palms.

Conclusions

Google Books search results yield these first-occurrence dates for the four spellings I researched: coco (1638), cacao (1662), cocao (1677), cocoa [coconut] (1694), and cocoa [cacao] (1698).

From this chronology it seems clear that Samuel Johnson's Dictionary of the English Language (1756) can't be blamed for causing the confusion over what word meant what thing. Nor did his 1756 dictionary run together the entries for coco and cocoa; it merely assigned the spelling cocoa to the coconut palm and ignored the cacao plant altogether.

Still, it is difficult to explain why a man who in 1735 was happily using the word coco to refer to the coconut palm should decide in 1756 to insist on spelling it cocoa and thus invite confusion between coconut cocoa and cacao cocoa—the latter being a usage he was undoubtedly familiar with from living in London during the heyday of the famous Cocoa Tree chocolate house.

In Johnson's favor is the fact that coconut cocoa seems to have been slightly older than cacao cocoa in English—but coco and cacao were even older and also had the advantage of being unambiguous. Perhaps Johnson was swayed by the use of cocoa in the coconut sense by Miller and Hill, the two sources he cites at the end of the entry for cocoa; I couldn't identify Hill, but Miller appears to be Philip Miller, author of The Gardeners Dictionary, which ran through eight editions between 1735 and 1768, and which seems to apply the spelling cocoa to the coconut palm from the outset.

But even if Johnson was convinced that cocoa was the proper spelling for the coconut palm, the language would have been better served if he had included an entry for cocao as well—instead of denying that word an entry and merely mentioning it twice in his definition of chocolate.

Today the standard formulations in English are coconut and cocoa bean; but if usage had evolved slightly differently during the 1600s and 1700s, we might instead be referring in everyday English to coco and cacao.