Alabama carried out on Thursday the first execution using nitrogen gas in the United States, an untested method that was the subject of debate before it was used. The inmate, Kenneth Smith, was pronounced dead at 8:25 p.m. Central time at the William C. Holman Correctional Facility in Atmore, Ala., after the U.S. Supreme Court denied an appeal to stay the execution.

Here are a few things to know about the case.

Who was Kenneth Smith, and what was his crime?

Kenneth Eugene Smith, 58, was one of three men convicted in the stabbing murder of Elizabeth Dorlene Sennett, 45, whose husband, a pastor, had recruited them to kill her in March 1988 in Colbert County, Ala.

According to court documents, Ms. Sennett, a mother of two, was stabbed 10 times in the attack by Mr. Smith and another man. Charles Sennett Sr., Ms. Sennett’s husband, had recruited a man to handle her killing, who in turn recruited Mr. Smith and another man.

Mr. Sennett arranged the murder in part to collect on an insurance policy that he had taken out on his wife, according to court records. He had promised the men $1,000 each for the killing.

What were the circumstances around his death sentence?

Mr. Smith was convicted in 1996. At his sentencing, 11 out of 12 jurors voted to spare his life and to sentence him to life in prison, but the judge in the case, N. Pride Tompkins, decided to overrule their decision and condemned him to death.

In 2017, Alabama stopped allowing judges to overrule death penalty juries in such a way, and such rulings are no longer allowed anywhere in the United States.

Mr. Smith, who was 22 years old at the time of the crime, had said that he did not believe that it was just for the judge to override the jury’s sentence in his case.

In a statement, Gov. Kay Ivey of Alabama previously said that while Alabama had made a “necessary” change to ban judges from overruling jurors’ recommendations, lawmakers had chosen not to make the law retroactive in order to honor sentences that had already been handed down and the victims’ relatives who were relying on them for justice.

What happened to Ms. Sennett’s husband and the others?

Mr. Sennett killed himself shortly after the murder of his wife.

One of the other men involved in the murder, John Forrest Parker, was executed by lethal injection in 2010, and another, Billy Gray Williams, was sentenced to life in prison and died behind bars in 2020.

The state tried to execute Mr. Smith before. What happened?

In November 2022, the state tried to execute Mr. Smith using lethal injection. But that night, a team of correctional facility workers tried and repeatedly failed to insert an intravenous line into Mr. Smith’s arms and hands and, eventually, a vein near his heart.

Finally, after multiple attempts, prison officials decided that they did not have the time to carry out the execution before the death warrant expired at midnight.

What is known about this method using nitrogen?

The method, known as nitrogen hypoxia, has been used in assisted suicides in Europe. Mr. Smith was fitted with a mask and administered a flow of nitrogen gas, effectively depriving him of oxygen until he dies.

Lawyers for the state argued that death by nitrogen hypoxia is painless, with unconsciousness occurring in a matter of seconds, followed by stoppage of the heart.

They also noted that Mr. Smith and his lawyers themselves identified the method as preferable to the troubled practice of lethal injection in the state.

But before the execution, Mr. Smith’s lawyers argued that Alabama was not adequately prepared to carry out the execution, and that a mask — rather than a bag or other enclosure — could allow in enough oxygen to prolong the process and cause suffering.

On Thursday, Alabama officials said the process had proved to be effective and humane.

State lawyers had previously claimed in court filings that an execution by nitrogen would ensure “unconsciousness in seconds.” But Mr. Smith appeared conscious for several minutes after the nitrogen gas began entering his mask, according to a report from Alabama journalists who witnessed the execution. He then “shook and writhed” before breathing heavily for several minutes. Eventually, his breathing slowed, then stopped.

Lee Hedgepeth, a reporter who witnessed the execution, said Mr. Smith’s head moved back and forth violently in the minutes after the execution began.

But John Q. Hamm, the state prison system’s commissioner, downplayed Mr. Smith’s body movements, saying “nothing was out of the ordinary from what we were expecting.”

What was the stance of the victim’s family?

“Some of these people out there say, ‘Well, he doesn’t need to suffer like that,’” Charles Sennett Jr., one of Ms. Sennett’s sons, told the local station WAAY31 this month. “Well, he didn’t ask Mama how to suffer. They just did it. They stabbed her multiple times.”

Another son, Michael Sennett, told NBC News in December that he was frustrated that the state had taken so long to carry out an execution that the judge ordered decades ago.

“It doesn’t matter to me how he goes out, so long as he goes,” he said, noting that Mr. Smith had been in prison “twice as long as I knew my mom.”