Compton said Cynthia Darlene Stout, 43, told authorities that her boyfriend was trying to throw the substance on her during an argument in their pickup truck and that it hit the children instead.
Compton said that they are preparing charges against the man, who has not yet been arrested.
Stout was arrested Wednesday on a charge of child endangerment after three of her children, ages 14, 7 and 4, were badly burned by the acid. Compton said Stout tried to walk away from the truck near a cafe in Woodbine while the man took the 18-month-old to a nearby residence where a woman washed down the infant with water.
Deputies were able to locate the 18-month-old through witnesses at the scene, Compton said, adding that Stout was apprehended while trying to leave the cafe without the three older children. He said she had walked 500 to 600 yards down the road when she was caught by police.
Stout remained in jail Thursday afternoon on a $100,000 bond. A jail official said an attorney was not listed for Stout.
All four children were flown by air ambulance to Parkland Memorial Hospital in Dallas. A Parkland spokeswoman said Thursday that they could not release any information on the patients.
Compton said it was unclear why sulfuric acid was in the truck. He said Stout told authorities the chemical was for a clogged drain.
Woodbine is an unincorporated community more than 60 miles north of Dallas.
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