The death chamber in Arkansas, where as many as seven inmates may be executed by the end of April. PHOTOGRAPH BY DANNY JOHNSTON / AP

The state of Arkansas plans to execute seven death-row inmates between Monday and the end of the month. Since 1976, when the Supreme Court reinstated capital punishment, no state has executed so many people in such a short period of time. In late March, the inmates asked the Supreme Court to hear their cases on the ground that Arkansas’s hurried schedule was “an affront” to their “basic human dignity.” The Justices are expected to consider the petition on Thursday, four days before the first two executions are slated to take place—but the prospects for the Court taking action are not good.

In a court filing, the inmates’ lawyers have argued that the schedule, along with other dangerous aspects of the planned executions, create “a substantial and objectively intolerable risk of suffering and harm” to the inmates—in other words, they believe the plan to be cruel and unusual, and therefore unconstitutional. They are particularly concerned about the state’s sourcing and use of the sedative midazolam as the first of three drugs in its lethal-injection procedure, which also includes vecuronium bromide, to cause paralysis, and potassium chloride, to stop the heart.

Lethal injection has been defended as a relatively quick, painless way to kill, but four states—Ohio, Oklahoma, Arizona, and Alabama—have in recent years carried out executions in which midazolam failed to keep inmates unconscious. These botched executions saw inmates gasping for breath, snorting, writhing, convulsing, and otherwise showing that they were conscious and in excruciating pain—one of these executions dragged on for almost two hours. In 2015, in a dissent to a Supreme Court ruling about lethal-injection drugs, Justice Sonia Sotomayor noted that, when midazolam does not work the way corrections officials want it to, the drugs that then paralyze an inmate and stop his heart “do so in a torturous manner, causing burning, searing pain.” She described that as “what may well be the chemical equivalent of being burned at the stake.”

Since these incidents, Arizona, Florida, and Kentucky have removed midazolam from their execution procedures. In January, a federal magistrate judge in Ohio blocked the state from using a new three-drug combination for lethal injection, because he determined that the use of midazolam created a “substantial risk of harm.” Arkansas, however, is not only using midazolam in its procedures this month, it is apparently letting its stock of midazolam—which has a use-by date of late April—dictate its execution schedule.

Asa Hutchinson, the state’s governor, has suggested that he had no alternative but to approve the schedule. In February, at a press conference given after he signed the death warrants, he said, “I would love to have those extended over a period of multiple months and years, but that’s not the circumstances that I find myself in.” Hutchinson did not explicitly say what he meant by “circumstances,” but the state has hinted that it is worried it would have a difficult time obtaining a fresh supply of midazolam if it let its current stock expire. In 2015, Wendy Kelley, the director of the Arkansas Department of Correction, said that the seller of the state’s “current supply of execution drugs has made clear to me that it will not supply any additional drugs for the A.D.C. to use in executions.” She also said that she was “unaware of the identity of any supplier or manufacturer of drugs that will sell them to the A.D.C. for use in executions.”

Midazolam is available as a generic drug and is not expensive—it is on the World Health Organization’s “List of Essential Medicines” as a sedative for short-term medical procedures. But major drug manufacturers, including Pzifer and Teva, have stopped selling drugs for use in lethal injections, forcing states to turn to other sources, like local compounding pharmacies—which typically combine, mix, or alter drugs to meet the need of individual patients—for the production of these drugs. The F.D.A. does not approve products made by a compounding pharmacy, and a basic requirement of having a drug compounded is a medical prescription for a patient. Both of these facts raise questions about states using these pharmacies as sources for lethal-injection drugs.

Arkansas had, until recently, planned to execute eight inmates this month—then, last week, the Arkansas parole board recommended clemency for one of the men, and a federal judge stayed his execution. Four of the seven inmates who remain scheduled, meanwhile, appear to suffer from serious mental illness or intellectual impairment, according to the Fair Punishment Project, which is affiliated with Harvard Law School. The Supreme Court has said that these conditions should exempt from a death sentence an individual convicted of a capital crime. And one of the inmates recently had his case taken up by lawyers from the Innocence Project, which has used DNA evidence to prove the innocence of nineteen death-row inmates. In a report released late last month, the Fair Punishment Project advised, “The Governor should declare a moratorium on executions so these legal deficiencies can be given a closer look, or else the Courts must intervene to stop these executions in order to preserve public confidence in the rule of law.”

Arkansas executed twenty-seven people between 1990 and the end of 2005, but has not carried out an execution since. This twelve-year execution hiatus has been the result of a period of intense debate about lethal injection in the state’s court system, legislature, and governor’s office. In a forthcoming article in the Arkansas Law Review, Julie Vandiver, an assistant federal public defender in the capital-habeas unit for eastern Arkansas, writes that, in the past decade, twenty-one execution dates have been set in Arkansas, only to be stayed by a court. Nineteen of those stays have been due to litigation about lethal injection. As Vandiver explains in her article, Arkansas saw four botched lethal-injection executions between 1990 and 2005. One inmate started to cough three minutes into his execution, and turned blue. The execution of another inmate took sixty-nine minutes—it took the execution team fifty minutes to find a suitable vein before administering the drugs. A third had what appeared to be a seizure. A fourth was still talking when she should have been unconscious.

In 2012, the Arkansas Supreme Court struck down a state statute called the Method of Execution Act, ruling that it didn’t provide the state’s correction department with sufficient guidelines for carrying out lethal injections. But, as Vandiver writes, because of the ruling, “The Arkansas Supreme Court decision left the State without a way to execute prisoners.” Years of legal and legislative wrangling followed, during which the state legislature amended the state capital-punishment statute twice. In 2015, lawmakers gave the state correction department the option of executing inmates using either a barbiturate or the three-drug combination of midazolam, vecuronium bromide, and potassium chloride. They also, according to Vandiver, authorized the state to buy drugs made by compounding pharmacies, and to keep secret the identity of “the compounding pharmacy, testing laboratory, seller, or supplier” of any drug.

Because Arkansas has recently been able to procure both vecuronium bromide and potassium chloride after running out, it is striking that the state now apparently wants to avoid having to obtain fresh midazolam. A new batch of midazolam would allow the state to space out its execution schedule. The state’s actions suggest that drug makers’ opposition to the use of their medicines in lethal injections is having an effect—but it is an effect that also comes with risks.

On Tuesday, the president of the American Bar Association asked Hutchinson to delay his “unprecedented execution schedule” because “expediency need not, and should not, be placed above the Constitution’s due process protections.” Earlier this week, a federal judge began to hear arguments from the inmates’ lawyers about the risks involved in using midazolam and in following the accelerated schedule. The lawyers have presented evidence that the schedule is making it impossible for them to defend their clients properly, depriving the inmates of their right to counsel and leaving the lawyers in violation of their ethical duties. Meanwhile, all eyes remain on Hutchinson—the only official with the power to grant these inmates clemency. I e-mailed Julie Vandiver to ask her to explain the significance of Arkansas’s long debate about lethal injection and capital punishment. She replied, “When the state undertakes the task of killing a person, there are multiple ways that it can go horribly wrong. Over and over, Arkansas officials have failed to treat this incredibly complex enterprise with appropriate gravity.”